A342797 Irregular triangle read by rows: T(n, k) is the k-th antidiagonal sum of the n X n matrices defined in A069480 and A078475.

1, 1, 5, 4, 1, 5, 15, 15, 9, 1, 5, 15, 34, 36, 29, 16, 1, 5, 15, 34, 65, 70, 63, 47, 25, 1, 5, 15, 34, 65, 111, 120, 114, 96, 69, 36, 1, 5, 15, 34, 65, 111, 175, 189, 185, 166, 135, 95, 49, 1, 5, 15, 34, 65, 111, 175, 260, 280, 279, 260, 226, 180, 125, 64

Offset: 1

Author

Stefano Spezia, Apr 25 2021

Keywords

• nonn
• tabf

Examples

			The triangle T(n, k) begins:
1
1    5    4
1    5   15   15    9
1    5   15   34   36   29   16
1    5   15   34   65   70   63   47   25
...
		

Crossrefs

Cf. A000290 (diagonal), A006003, A037270 (row sums), A060747 (row length), A069480, A078475.

Programs

Mathematica

T[n_,k_]:=If[k<=n,(k+k^3)/2,(k^3+2n-6k^2n-4n^3+k(10n^2-1))/2]; Flatten[Table[T[n,k],{n,8},{k,2n-1}]]

Formula

T(n, k) = A006003(k) for 1 <= k <= n.

T(n, k) = (k^3 + 2*n - 6*k^2*n - 4*n^3 + k*(10*n^2 - 1))/2 for n < k <= 2*n - 1.

T(n, 2*n-1) = A000290(n).