A036814 Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5)).

1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 8, 6, 11, 12, 14, 24, 21, 31, 37, 40, 69, 59, 87, 100, 112, 178, 160, 223, 259, 284, 443, 399, 549, 629, 694, 1035, 961, 1277, 1467, 1609, 2339, 2195, 2874, 3276, 3601, 5084, 4854, 6222, 7088, 7767, 10745, 10358, 13100, 14854

Offset

0,6

Comments

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

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

Links

Table of n, a(n) for n=0..53.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[1] == c[4] && 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, 1, 45}] (* Jean-François Alcover, Oct 10 2024 *)

Crossrefs

Sequence in context: A242971 A036818 A036813 * A137776 A262699 A153946

Adjacent sequences: A036811 A036812 A036813 * A036815 A036816 A036817

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved