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

1,3

Links

Table of n, a(n) for n=1..64.

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).

Example

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
...

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}]]

Crossrefs

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

Sequence in context: A113011 A028875 A130815 * A084129 A011503 A296498

Adjacent sequences: A342794 A342795 A342796 * A342798 A342799 A342800

Keyword

nonn,tabf

Author

Stefano Spezia, Apr 25 2021

Status

approved