A036817 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A036817

Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).

1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 6, 4, 8, 8, 10, 19, 15, 22, 27, 28, 55, 42, 65, 74, 82, 141, 117, 169, 196, 210, 350, 296, 420, 479, 521, 812, 723, 977, 1121, 1215, 1831, 1657, 2203, 2504, 2728, 3971, 3676, 4763, 5419, 5888, 8389, 7847, 10030, 11350, 12353

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

OFFSET

0,7

COMMENTS

For a given partition cn(i,n) means the number of its parts equal to i modulo n.

Short: (1=4 and 0<=2 and 0<=3 and 1<=2 and 1<=3).

LINKS

Table of n, a(n) for n=0..54.

MATHEMATICA

okQ[p_] := Module[{c},

c[k_] := c[k] = Count[Mod[p, 5], k];

c[1] == c[4] && c[0] <= c[2] &&

c[0] <= c[3] && c[1] <= c[2] &&

c[1] <= c[3]];

a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];

Table[Print[n, " ", a[n]]; a[n], {n, 0, 54}] (* Jean-François Alcover, Oct 11 2024 *)

CROSSREFS

Sequence in context: A372007 A051715 A143269 * A239962 A175175 A116417

Adjacent sequences: A036814 A036815 A036816 * A036818 A036819 A036820

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

a(0)=1 prepended by Jean-François Alcover, Oct 11 2024

STATUS

approved