A156044 Triangle read by rows: T(n,k) = 2 + A000041(n) - A000041(k) - A000041(n-k).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 3, 4, 4, 3, 1, 1, 5, 6, 7, 6, 5, 1, 1, 5, 8, 9, 9, 8, 5, 1, 1, 8, 11, 14, 14, 14, 11, 8, 1, 1, 9, 15, 18, 20, 20, 18, 15, 9, 1, 1, 13, 20, 26, 28, 30, 28, 26, 20, 13, 1, 1, 15, 26, 33, 38, 40, 40, 38, 33, 26, 15, 1

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Example

Triangle begins:
  1;
  1,  1;
  1,  2,  1;
  1,  2,  2,  1;
  1,  3,  3,  3,  1;
  1,  3,  4,  4,  3,  1;
  1,  5,  6,  7,  6,  5,  1;
  1,  5,  8,  9,  9,  8,  5,  1;
  1,  8, 11, 14, 14, 14, 11,  8,  1;
  1,  9, 15, 18, 20, 20, 18, 15,  9,  1;
  1, 13, 20, 26, 28, 30, 28, 26, 20, 13, 1;
  ...

Mathematica

A156044[n_, k_] := 2 + #[n] - #[k] - #[n - k] & [PartitionsP[#] &];
Table[A156044[n, k], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Nov 20 2025 *)

Prog

(PARI) T(n, k) = 2 + numbpart(n) - numbpart(k) - numbpart(n-k); \\ Andrew Howroyd, Nov 19 2025

Crossrefs

Cf. A000041.

Sequence in context: A103441 A081206 A333161 * A180980 A275298 A048570

Adjacent sequences: A156041 A156042 A156043 * A156045 A156046 A156047

Keyword

nonn,tabl

Author

Roger L. Bagula, Feb 02 2009

Status

approved