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

0,2

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, ...).

Links

Table of n, a(n) for n=0..77.

Example

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;
  ...

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 *)

Crossrefs

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

Sequence in context: A357217 A353595 A317086 * A025840 A188542 A029284

Adjacent sequences: A131373 A131374 A131375 * A131377 A131378 A131379

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jul 04 2007

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

Status

approved