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URL: https://oeis.org/A156054

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A156054

Triangle read by rows: T(n,k) = 2 + A000009(n) - A000009(k) - A000009(n-k).

1

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 2, 3, 3, 4, 3, 3, 2, 1, 1, 3, 4, 4, 5, 5, 4, 4, 3, 1, 1, 3, 5, 5, 6, 6, 6, 5, 5, 3, 1, 1, 3, 5, 6, 7, 7, 7, 7, 6, 5, 3, 1, 1, 4, 6, 7, 9, 9, 9, 9, 9, 7, 6, 4, 1

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

OFFSET

0,8

LINKS

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

EXAMPLE

Triangle begins:

1;

1, 1;

1, 1, 1;

1, 2, 2, 1;

1, 1, 2, 1, 1;

1, 2, 2, 2, 2, 1;

1, 2, 3, 2, 3, 2, 1;

1, 2, 3, 3, 3, 3, 2, 1;

1, 2, 3, 3, 4, 3, 3, 2, 1;

1, 3, 4, 4, 5, 5, 4, 4, 3, 1;

1, 3, 5, 5, 6, 6, 6, 5, 5, 3, 1;

...

MATHEMATICA

f[n_, m_] = 2 + PartitionsQ[n] - PartitionsQ[m] - PartitionsQ[n - m];

Table[Table[f[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

PROG

(PARI) \\ here b(n) is A000009.

b(n) = my(A=O(x*x^n)); polcoef( eta(x^2 + A) / eta(x + A), n);

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

CROSSREFS

Sequence in context: A212810 A072344 A140500 * A030616 A066422 A274888

Adjacent sequences: A156051 A156052 A156053 * A156055 A156056 A156057

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 02 2009

STATUS

approved