A036805 Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

1, 1, 1, 1, 2, 3, 4, 4, 5, 7, 12, 14, 16, 18, 25, 38, 45, 49, 58, 76, 111, 128, 143, 165, 214, 295, 340, 378, 439, 552, 745, 849, 948, 1092, 1357, 1778, 2020, 2249, 2588, 3166, 4078, 4601, 5129, 5871, 7112, 8996, 10118, 11254, 12854, 15407, 19234, 21541, 23947

Offset

0,5

Comments

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

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

Links

Table of n, a(n) for n=0..52.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[2] == c[3] &&
   c[0] <= c[1] &&
   c[0] <= c[4]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)

Crossrefs

Sequence in context: A036807 A036808 A103750 * A036804 A180046 A008329

Adjacent sequences: A036802 A036803 A036804 * A036806 A036807 A036808

Keyword

nonn,changed

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 10 2024

Status

approved