A376335 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,3

LINKS

Table of n, a(n) for n=2..82.

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.

FORMULA

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

EXAMPLE

The triangle begins as:

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;

...

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