A036811 Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).

1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 8, 9, 11, 12, 16, 26, 29, 31, 37, 48, 76, 82, 90, 103, 136, 199, 218, 237, 274, 349, 495, 542, 593, 679, 855, 1165, 1281, 1399, 1602, 1981, 2642, 2893, 3172, 3613, 4420, 5770, 6313, 6913, 7862, 9505, 12234, 13345, 14619, 16558

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 and 2<=1 and 2<=4).

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[2] == c[3] && c[0] <= c[1] &&
   c[0] <= c[4] && c[2] <= c[1] &&
   c[2] <= 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: A147663 A301765 A374210 * A330265 A302163 A302635

Adjacent sequences: A036808 A036809 A036810 * A036812 A036813 A036814

Keyword

nonn

Author

Olivier Gérard

Extensions

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

Status

approved