Ctree
A106465 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ is(n \text{ odd})\ ? \ 1 : (k + 1) \text{ mod } 2 } \)
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 1 2 1 1 2 1 2 3 4 1 1 2 2 3 1 2 3 4 5
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 0 2 1 2 3 0 2 0 4 1 2 3 4 5 0 2 0 4 0
\(\sum_{k=0}^{n} T_{n, k} \ 2^{n - k} \) ➤ PosHalf ➤ 1 3 5 15 21 63 85 255 341 1023 1365
\(\sum_{k=0}^{n} T_{n, k} \ k^{2}\) ➤ TransSqrs ➤ 0 1 4 14 20 55 56 140 120 285 220 506
\(\sum_{k=0}^{n} T_{n, k}\ 2^k\) ➤ PolyCol2 ➤ 1 3 5 15 21 63 85 255 341 1023 1365
\(\sum_{k=0}^{n} T_{n, k}\ 3^k\) ➤ PolyCol3 ➤ 1 4 10 40 91 364 820 3280 7381 29524
\(\sum_{k=0}^{n} T_{n, k}\ n^k\) ➤ PolyDiag ➤ 1 2 5 40 273 3906 47989 960800 17043521
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 2 1 1 2 1 2 3 4 1 1 2 2 3 1 2 3 4 5
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 1 0 2 1 2 3 0 2 0 4 1 2 3 4 5 0 2 0 4 0
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 1 4 14 20 55 56 140 120 285 220 506
\(\sum_{k=0}^{n} T_{n, n-k}\ 3^k\) ➤ RevPolyCol3 ➤ 1 4 10 40 91 364 820 3280 7381 29524
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 2 5 40 273 3906 47989 960800 17043521