A131376 Triangle read by rows: T(n,k) = A007318(n,k) + A065941(n,k) - A168561(n,k).

1, 2, 1, 1, 3, 1, 2, 2, 5, 1, 1, 5, 6, 6, 1, 2, 3, 14, 9, 8, 1, 1, 7, 14, 24, 16, 9, 1, 2, 4, 27, 30, 45, 21, 11, 1, 1, 9, 25, 62, 70, 66, 31, 12, 1, 2, 5, 44, 71, 147, 120, 104, 38, 14, 1, 1, 11, 39, 128, 203, 273, 217, 140, 51, 15, 1, 2, 6, 65, 139, 366, 434, 518, 329, 200, 60, 17, 1

Offset: 0

Author

Gary W. Adamson, Jul 04 2007

Keywords

• nonn
• tabl
• easy

Comments

The old definition was: A007318 + A065941 - A049310. - N. J. A. Sloane, Aug 09 2019

Row sums = A117591: (1, 3, 5, 10, 19, 37, 72, ...).

Examples

			First few rows of the triangle are:
  1;
  2, 1;
  1, 3, 1;
  2, 2, 5, 1;
  1, 5, 6, 6, 1;
  2, 3, 14, 9, 8, 1;
  1, 7, 14, 24, 16, 9, 1;
  ...
		

Crossrefs

Cf. A007318, A065941, A049310, A117591 (row sums), A131375, A168561, A309213.

Programs

Mathematica

Table[Binomial[n, k] + Binomial[n - Floor[(k+1)/2], Floor[k/2]] - If[EvenQ[n+k], Binomial[(n+k)/2, k], 0], {n, 0, 11}, {k, 0, n}] // Flatten  (* Amiram Eldar, May 31 2025 *)

Extensions

The old definition of A131376 did not match its data, as Michel Marcus pointed out. The definition has been corrected here, keeping the data. The old definition with corrected data is now A309213. - N. J. A. Sloane, Aug 09 2019

More terms from Amiram Eldar, May 31 2025