The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A237825 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A237825

Number of partitions of n such that 3*(least part) = greatest part.
(history; published version)

#21 by Michael De Vlieger at Thu May 30 06:55:31 EDT 2024

STATUS

reviewed

approved

#20 by Stefano Spezia at Thu May 30 04:43:47 EDT 2024

STATUS

proposed

reviewed

#19 by Jean-François Alcover at Thu May 30 04:41:47 EDT 2024

STATUS

editing

proposed

#18 by Jean-François Alcover at Thu May 30 04:41:38 EDT 2024

MATHEMATICA

kmax = 57;

Sum[x^(4 k)/Product[1 - x^j, {j, k, 3 k}], {k, 1, kmax}]/x + O[x]^kmax // CoefficientList[#, x]& (* Jean-François Alcover, May 30 2024, after Seiichi Manyama *)

STATUS

approved

editing

#17 by Harvey P. Dale at Sun May 14 13:25:39 EDT 2023

STATUS

editing

approved

#16 by Harvey P. Dale at Sun May 14 13:25:36 EDT 2023

MATHEMATICA

Table[Count[IntegerPartitions[n], _?(3#[[-1]]==#[[1]]&)], {n, 60}] (* Harvey P. Dale, May 14 2023 *)

#15 by Seiichi Manyama at Sun May 14 11:51:55 EDT 2023

CROSSREFS

Cf. A000041, A117086, A237757, A237828, A237829.

#14 by Seiichi Manyama at Sun May 14 11:32:10 EDT 2023

CROSSREFS

Cf. A000041, A237757, A237826, A237827, A237828, A237829.

Cf. A118096, A237826, A237827.

#13 by Seiichi Manyama at Sun May 14 11:26:52 EDT 2023

FORMULA

G.f.: Sum_{k>=1} x^(4*k)/Product_{j=k..3*k} (1-x^j). - Seiichi Manyama, May 14 2023

#12 by Seiichi Manyama at Sun May 14 11:21:28 EDT 2023

PROG

(PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/prod(j=k, 3*k, 1-x^j)))) \\ _Seiichi Manyama_, May 14 2023