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

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