The On-Line Encyclopedia of Integer Sequences (OEIS)

A213260 revision #21

A213260

p(5n+4) where p(k) = number of partitions of k = A000041(k).

5, 30, 135, 490, 1575, 4565, 12310, 31185, 75175, 173525, 386155, 831820, 1741630, 3554345, 7089500, 13848650, 26543660, 49995925, 92669720, 169229875, 304801365, 541946240, 952050665, 1653668665, 2841940500, 4835271870, 8149040695, 13610949895, 22540654445, 37027355200, 60356673280, 97662728555, 156919475295

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OFFSET

0,1

COMMENTS

It is known that a(n) is divisible by 5 (see A071734).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

James Grime and Brady Haran, Partitions, Numberphile video (2016).

Lasse Winquist, An elementary proof of p(11m+6) == 0 (mod 11), J. Combinatorial Theory 6 1969 56--59. MR0236136 (38 #4434). - From N. J. A. Sloane, Jun 07 2012

FORMULA

a(n) = A000041(A016897(n)). - Omar E. Pol, Jan 18 2013

MATHEMATICA

Table[PartitionsP[5n+4], {n, 0, 40}] (* Harvey P. Dale, May 30 2013 *)

PROG

(PARI) a(n) = numbpart(5*n+4); \\ Michel Marcus, Jan 07 2015

(Python)

from sympy.ntheory import npartitions

def a(n): return npartitions(5*n+4)

print([a(n) for n in range(33)]) # Michael S. Branicky, May 30 2021

CROSSREFS

Cf. A000041, A071734, A213256, A076394.