NICOMACHUS[0] 1
[1] 2, 3
[2] 4, 6, 9
[3] 8, 12, 18, 27
[4] 16, 24, 36, 54, 81
[5] 32, 48, 72, 108, 162, 243

      OEIS Similars: A036561, A081954, A175840

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA0365611 2 3 4 6 9 8 12 18 27 16 24 36 54 81 32 48 72 108 162 243 64 96 144 216 324 486 729 128 192 288
StdRevT(n, n - k), 0 ≤ k ≤ nA1758401 3 2 9 6 4 27 18 12 8 81 54 36 24 16 243 162 108 72 48 32 729 486 324 216 144 96 64 2187 1458 972
StdAccsee docsA2304351 2 5 4 10 19 8 20 38 65 16 40 76 130 211 32 80 152 260 422 665 64 160 304 520 844 1330 2059 128
StdAccRevsee docsmissing1 3 5 9 15 19 27 45 57 65 81 135 171 195 211 243 405 513 585 633 665 729 1215 1539 1755 1899 1995
StdAntiDiagsee docsmissing1 2 4 3 8 6 16 12 9 32 24 18 64 48 36 27 128 96 72 54 256 192 144 108 81 512 384 288 216 162 1024
StdDiffx1T(n, k) (k+1)missing1 2 6 4 12 27 8 24 54 108 16 48 108 216 405 32 96 216 432 810 1458 64 192 432 864 1620 2916 5103
StdRowSum k=0..n T(n, k)A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
StdEvenSum k=0..n T(n, k) even(k)missing1 2 13 26 133 266 1261 2522 11605 23210 105469 210938 953317 1906634 8596237 17192474 77431669
StdOddSum k=0..n T(n, k) odd(k)missing0 3 6 39 78 399 798 3783 7566 34815 69630 316407 632814 2859951 5719902 25788711 51577422 232295007
StdAltSum k=0..n T(n, k) (-1)^kA0154411 -1 7 -13 55 -133 463 -1261 4039 -11605 35839 -105469 320503 -953317 2876335 -8596237 25854247
StdAbsSum k=0..n | T(n, k) |A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
StdDiagSum k=0..n // 2 T(n - k, k)A1677621 2 7 14 37 74 175 350 781 1562 3367 6734 14197 28394 58975 117950 242461 484922 989527 1979054
StdAccSum k=0..n j=0..k T(n, j)A0668101 7 33 131 473 1611 5281 16867 52905 163835 502769 1532883 4651897 14070379 42456897 127894979
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 8 43 194 793 3044 11191 39878 138805 474440 1598419 5322602 17553937 57428396 186601327 602785166
StdRowLcmLcm k=0..n | T(n, k) | > 1A0004001 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdRowMaxMax k=0..n | T(n, k) |A0002441 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163
StdColMiddleT(n, n // 2)A0265491 2 6 12 36 72 216 432 1296 2592 7776 15552 46656 93312 279936 559872 1679616 3359232 10077696
StdCentralET(2 n, n)A0004001 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
StdCentralOT(2 n + 1, n)A1677472 12 72 432 2592 15552 93312 559872 3359232 20155392 120932352 725594112 4353564672 26121388032
StdColLeftT(n, 0)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
StdColRightT(n, n)A0002441 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163
StdBinConv k=0..n C(n, k) T(n, k)A0003511 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdTransNat0 k=0..n T(n, k) kmissing0 3 24 129 582 2379 9132 33573 119634 416415 1423320 4795257 15967806 52661811 172285188 559803981
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 8 43 194 793 3044 11191 39878 138805 474440 1598419 5322602 17553937 57428396 186601327 602785166
StdTransSqrs k=0..n T(n, k) k^2missing0 3 42 327 1950 9975 46194 199551 819006 3232335 12369570 46173927 168875358 607191303 2151844530
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA0050611 7 37 175 781 3367 14197 58975 242461 989527 4017157 16245775 65514541 263652487 1059392917
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0534041 -1 13 -25 181 -481 2653 -8425 40261 -141361 624493 -2320825 9814741 -37664641 155441533
StdDiagRow1T(n + 1, n)A0087762 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814 86093442
StdDiagRow2T(n + 2, n)A0039464 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292 19131876 57395628 172186884
StdDiagRow3T(n + 3, n)A0050518 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528 12754584 38263752 114791256
StdDiagCol1T(n + 1, 1)A0072833 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304 196608 393216 786432 1572864
StdDiagCol2T(n + 2, 2)A0050109 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864 73728 147456 294912 589824 1179648 2359296
StdDiagCol3T(n + 3, 3)A17580627 54 108 216 432 864 1728 3456 6912 13824 27648 55296 110592 221184 442368 884736 1769472 3538944
StdPolysee docsmissing1 2 1 4 5 1 8 19 8 1 16 65 52 11 1 32 211 320 103 14 1 64 665 1936 935 172 17 1 128 2059 11648 8431
StdPolyRow1 k=0..1 T(1, k) n^kA0167892 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80 83 86 89 92 95 98 101
StdPolyRow2 k=0..2 T(2, k) n^kmissing4 19 52 103 172 259 364 487 628 787 964 1159 1372 1603 1852 2119 2404 2707 3028 3367 3724 4099 4492
StdPolyRow3 k=0..3 T(3, k) n^kmissing8 65 320 935 2072 3893 6560 10235 15080 21257 28928 38255 49400 62525 77792 95363 115400 138065
StdPolyCol2 k=0..n T(n, k) 2^kA0161291 8 52 320 1936 11648 69952 419840 2519296 15116288 90698752 544194560 3265171456 19591036928
StdPolyCol3 k=0..n T(n, k) 3^kA0161331 11 103 935 8431 75911 683263 6149495 55345711 498111911 4483008223 40347076055 363123688591
StdPolyDiag k=0..n T(n, k) n^kmissing1 5 52 935 24880 876197 38263744 1990676795 120082160896 8235645283745 632667857142784
AltTriangleT(n, k), 0 ≤ k ≤ nA0365611 2 -3 4 -6 9 8 -12 18 -27 16 -24 36 -54 81 32 -48 72 -108 162 -243 64 -96 144 -216 324 -486 729
AltRevT(n, n - k), 0 ≤ k ≤ nA1758401 -3 2 9 -6 4 -27 18 -12 8 81 -54 36 -24 16 -243 162 -108 72 -48 32 729 -486 324 -216 144 -96 64
AltAccsee docsmissing1 2 -1 4 -2 7 8 -4 14 -13 16 -8 28 -26 55 32 -16 56 -52 110 -133 64 -32 112 -104 220 -266 463 128
AltAccRevsee docsmissing1 -3 -1 9 3 7 -27 -9 -21 -13 81 27 63 39 55 -243 -81 -189 -117 -165 -133 729 243 567 351 495 399
AltAntiDiagsee docsmissing1 2 4 -3 8 -6 16 -12 9 32 -24 18 64 -48 36 -27 128 -96 72 -54 256 -192 144 -108 81 512 -384 288
AltDiffx1T(n, k) (k+1)missing1 2 -6 4 -12 27 8 -24 54 -108 16 -48 108 -216 405 32 -96 216 -432 810 -1458 64 -192 432 -864 1620
AltRowSum k=0..n T(n, k)A0154411 -1 7 -13 55 -133 463 -1261 4039 -11605 35839 -105469 320503 -953317 2876335 -8596237 25854247
AltEvenSum k=0..n T(n, k) even(k)missing1 2 13 26 133 266 1261 2522 11605 23210 105469 210938 953317 1906634 8596237 17192474 77431669
AltOddSum k=0..n T(n, k) odd(k)missing0 -3 -6 -39 -78 -399 -798 -3783 -7566 -34815 -69630 -316407 -632814 -2859951 -5719902 -25788711
AltAltSum k=0..n T(n, k) (-1)^kA0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
AltAbsSum k=0..n | T(n, k) |A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
AltDiagSum k=0..n // 2 T(n - k, k)missing1 2 1 2 13 26 25 50 181 362 481 962 2653 5306 8425 16850 40261 80522 141361 282722 624493 1248986
AltAccSum k=0..n j=0..k T(n, j)missing1 1 9 5 65 -3 457 -347 3345 -4915 26009 -53451 213601 -526115 1824105 -4948027 15958193 -45515283
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -4 19 -70 265 -928 3247 -11002 37045 -122740 404059 -1317646 4273441 -13773640 44197255
AltRowLcmLcm k=0..n | T(n, k) | > 1A0004001 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltRowMaxMax k=0..n | T(n, k) |A0002441 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163
AltColMiddleT(n, n // 2)A0265491 2 -6 -12 36 72 -216 -432 1296 2592 -7776 -15552 46656 93312 -279936 -559872 1679616 3359232
AltCentralET(2 n, n)A0004001 -6 36 -216 1296 -7776 46656 -279936 1679616 -10077696 60466176 -362797056 2176782336 -13060694016
AltCentralOT(2 n + 1, n)A1677472 -12 72 -432 2592 -15552 93312 -559872 3359232 -20155392 120932352 -725594112 4353564672
AltColLeftT(n, 0)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
AltColRightT(n, n)A0002441 -3 9 -27 81 -243 729 -2187 6561 -19683 59049 -177147 531441 -1594323 4782969 -14348907 43046721
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0003511 -5 25 -125 625 -3125 15625 -78125 390625 -1953125 9765625 -48828125 244140625 -1220703125
AltTransNat0 k=0..n T(n, k) kmissing0 -3 12 -57 210 -795 2784 -9741 33006 -111135 368220 -1212177 3952938 -12820323 41320920 -132591765
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -4 19 -70 265 -928 3247 -11002 37045 -122740 404059 -1317646 4273441 -13773640 44197255
AltTransSqrs k=0..n T(n, k) k^2missing0 -3 30 -183 930 -4215 17814 -71535 276834 -1040655 3823590 -13787607 48952290 -171536007 594389910
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0534041 1 13 25 181 481 2653 8425 40261 141361 624493 2320825 9814741 37664641 155441533 607417225
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0050611 -7 37 -175 781 -3367 14197 -58975 242461 -989527 4017157 -16245775 65514541 -263652487 1059392917
AltDiagRow1T(n + 1, n)A0087762 -6 18 -54 162 -486 1458 -4374 13122 -39366 118098 -354294 1062882 -3188646 9565938 -28697814
AltDiagRow2T(n + 2, n)A0039464 -12 36 -108 324 -972 2916 -8748 26244 -78732 236196 -708588 2125764 -6377292 19131876 -57395628
AltDiagRow3T(n + 3, n)A0050518 -24 72 -216 648 -1944 5832 -17496 52488 -157464 472392 -1417176 4251528 -12754584 38263752
AltDiagCol1T(n + 1, 1)A007283-3 -6 -12 -24 -48 -96 -192 -384 -768 -1536 -3072 -6144 -12288 -24576 -49152 -98304 -196608 -393216
AltDiagCol2T(n + 2, 2)A0050109 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864 73728 147456 294912 589824 1179648 2359296
AltDiagCol3T(n + 3, 3)A175806-27 -54 -108 -216 -432 -864 -1728 -3456 -6912 -13824 -27648 -55296 -110592 -221184 -442368 -884736
AltPolysee docsmissing1 2 1 4 -1 1 8 7 -4 1 16 -13 28 -7 1 32 55 -160 67 -10 1 64 -133 976 -595 124 -13 1 128 463 -5824
AltPolyRow1 k=0..1 T(1, k) n^kA0167772 -1 -4 -7 -10 -13 -16 -19 -22 -25 -28 -31 -34 -37 -40 -43 -46 -49 -52 -55 -58 -61 -64 -67 -70 -73
AltPolyRow2 k=0..2 T(2, k) n^kmissing4 7 28 67 124 199 292 403 532 679 844 1027 1228 1447 1684 1939 2212 2503 2812 3139 3484 3847 4228
AltPolyRow3 k=0..3 T(3, k) n^kmissing8 -13 -160 -595 -1480 -2977 -5248 -8455 -12760 -18325 -25312 -33883 -44200 -56425 -70720 -87247
AltPolyCol2 k=0..n T(n, k) 2^kA0535241 -4 28 -160 976 -5824 35008 -209920 1259776 -7558144 45349888 -272097280 1632587776 -9795518464
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -7 67 -595 5371 -48307 434827 -3913315 35220091 -316980307 2852823787 -25675412035 231078712411
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 28 -595 17776 -670033 30611008 -1644472135 101607982336 -7099694210125 553584375000064
RevTriangleT(n, k), 0 ≤ k ≤ nA1758401 3 2 9 6 4 27 18 12 8 81 54 36 24 16 243 162 108 72 48 32 729 486 324 216 144 96 64 2187 1458 972
RevAccsee docsmissing1 3 5 9 15 19 27 45 57 65 81 135 171 195 211 243 405 513 585 633 665 729 1215 1539 1755 1899 1995
RevAccRevsee docsA2304351 2 5 4 10 19 8 20 38 65 16 40 76 130 211 32 80 152 260 422 665 64 160 304 520 844 1330 2059 128
RevAntiDiagsee docsmissing1 3 9 2 27 6 81 18 4 243 54 12 729 162 36 8 2187 486 108 24 6561 1458 324 72 16 19683 4374 972 216
RevDiffx1T(n, k) (k+1)missing1 3 4 9 12 12 27 36 36 32 81 108 108 96 80 243 324 324 288 240 192 729 972 972 864 720 576 448 2187
RevRowSum k=0..n T(n, k)A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
RevEvenSum k=0..n T(n, k) even(k)A1679101 3 13 39 133 399 1261 3783 11605 34815 105469 316407 953317 2859951 8596237 25788711 77431669
RevOddSum k=0..n T(n, k) odd(k)missing0 2 6 26 78 266 798 2522 7566 23210 69630 210938 632814 1906634 5719902 17192474 51577422 154863338
RevAltSum k=0..n T(n, k) (-1)^kA0154411 1 7 13 55 133 463 1261 4039 11605 35839 105469 320503 953317 2876335 8596237 25854247 77431669
RevAbsSum k=0..n | T(n, k) |A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
RevDiagSum k=0..n // 2 T(n - k, k)A1352471 3 11 33 103 309 935 2805 8431 25293 75911 227733 683263 2049789 6149495 18448485 55345711
RevAccSum k=0..n j=0..k T(n, j)missing1 8 43 194 793 3044 11191 39878 138805 474440 1598419 5322602 17553937 57428396 186601327 602785166
RevAccRevSum k=0..n j=0..k T(n, n - j)A0668101 7 33 131 473 1611 5281 16867 52905 163835 502769 1532883 4651897 14070379 42456897 127894979
RevRowLcmLcm k=0..n | T(n, k) | > 1A0004001 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevRowMaxMax k=0..n | T(n, k) |A0002441 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163
RevColMiddleT(n, n // 2)A0265321 3 6 18 36 108 216 648 1296 3888 7776 23328 46656 139968 279936 839808 1679616 5038848 10077696
RevCentralET(2 n, n)A0004001 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016
RevCentralOT(2 n + 1, n)A0813413 18 108 648 3888 23328 139968 839808 5038848 30233088 181398528 1088391168 6530347008 39182082048
RevColLeftT(n, 0)A0002441 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163
RevColRightT(n, n)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
RevBinConv k=0..n C(n, k) T(n, k)A0003511 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625
RevTransNat0 k=0..n T(n, k) kmissing0 2 14 66 262 946 3222 10562 33734 105810 327670 1005538 3065766 9303794 28140758 84913794
RevTransNat1 k=0..n T(n, k) (k + 1)A0668101 7 33 131 473 1611 5281 16867 52905 163835 502769 1532883 4651897 14070379 42456897 127894979
RevTransSqrs k=0..n T(n, k) k^2missing0 2 22 138 670 2810 10734 38474 131806 436890 1413070 4487018 14050878 43537082 133822510 408840330
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0161291 8 52 320 1936 11648 69952 419840 2519296 15116288 90698752 544194560 3265171456 19591036928
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0535241 -4 28 -160 976 -5824 35008 -209920 1259776 -7558144 45349888 -272097280 1632587776 -9795518464
RevDiagRow1T(n + 1, n)A0072833 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304 196608 393216 786432 1572864
RevDiagRow2T(n + 2, n)A0050109 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864 73728 147456 294912 589824 1179648 2359296
RevDiagRow3T(n + 3, n)A17580627 54 108 216 432 864 1728 3456 6912 13824 27648 55296 110592 221184 442368 884736 1769472 3538944
RevDiagCol1T(n + 1, 1)A0087762 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814 86093442
RevDiagCol2T(n + 2, 2)A0039464 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292 19131876 57395628 172186884
RevDiagCol3T(n + 3, 3)A0050518 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528 12754584 38263752 114791256
RevPolysee docsmissing1 3 1 9 5 1 27 19 7 1 81 65 37 9 1 243 211 175 63 11 1 729 665 781 405 97 13 1 2187 2059 3367 2511
RevPolyRow1 k=0..1 T(1, k) n^kA0054083 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69
RevPolyRow2 k=0..2 T(2, k) n^kmissing9 19 37 63 97 139 189 247 313 387 469 559 657 763 877 999 1129 1267 1413 1567 1729 1899 2077 2263
RevPolyRow3 k=0..3 T(3, k) n^kmissing27 65 175 405 803 1417 2295 3485 5035 6993 9407 12325 15795 19865 24583 29997 36155 43105 50895
RevPolyCol2 k=0..n T(n, k) 2^kA0050611 7 37 175 781 3367 14197 58975 242461 989527 4017157 16245775 65514541 263652487 1059392917
RevPolyCol3 k=0..n T(n, k) 3^kA0161371 9 63 405 2511 15309 92583 557685 3352671 20135709 120873303 725416965 4353033231 26119793709
RevPolyDiag k=0..n T(n, k) n^kmissing1 5 37 405 6505 142753 3981069 134162045 5286112081 238031144505 12047058813109 676579085816725
 << TableSourceSimilarsIndex >> 

Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.