A376335 Irregular triangle read by rows: T(n,k) = A008949(n-1,k) if 0 <= k <= n - 2 otherwise A008949(n-1,2*n-4-k) if n - 2 <= k <= 2*n - 4.

1, 1, 3, 1, 1, 4, 7, 4, 1, 1, 5, 11, 15, 11, 5, 1, 1, 6, 16, 26, 31, 26, 16, 6, 1, 1, 7, 22, 42, 57, 63, 57, 42, 22, 7, 1, 1, 8, 29, 64, 99, 120, 127, 120, 99, 64, 29, 8, 1, 1, 9, 37, 93, 163, 219, 247, 255, 247, 219, 163, 93, 37, 9, 1, 1, 10, 46, 130, 256, 382, 466, 502, 511, 502, 466, 382, 256, 130, 46, 10, 1

Offset: 2

Author

Stefano Spezia, Sep 20 2024

Keywords

• nonn
• easy
• tabf

Examples

			The triangle begins as:
  1;
  1, 3,  1;
  1, 4,  7,  4,  1;
  1, 5, 11, 15, 11,  5,  1;
  1, 6, 16, 26, 31, 26, 16,  6,  1;
  1, 7, 22, 42, 57, 63, 57, 42, 22, 7, 1;
  ...
		

Links

• Nsibiet E. Udo, Praise Adeyemo, Balazs Szendroi, and Stavros Argyrios Papadakis, Ideals, representations and a symmetrised Bernoulli triangle, arXiv:2409.10278 [math.AC], 2024. See p. 2.

Crossrefs

Cf. A000337, A008949.

Programs

Mathematica

b[n_,k_]:=Sum[Binomial[n,j],{j,0,k}]; T[n_,k_]:=If[0<=k<=n-2,b[n-1,k],b[n-1,2n-4-k]]; Table[T[n,k],{n,2,10},{k,0,2n-4}]//Flatten

Formula

Sum_{k=0..2*n-4} T(n,k) = A000337(n-1). [Udo et al.]