A036801 Number of partitions satisfying (cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 34, 44, 60, 76, 100, 128, 165, 207, 265, 330, 420, 519, 649, 799, 993, 1224, 1502, 1834, 2244, 2724, 3332, 4016, 4865, 5856, 7058, 8490, 10171, 12154, 14523, 17296, 20639, 24460, 29031, 34340, 40616, 47987, 56520, 66489, 78159

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

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

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

Crossrefs

Cf. A035959.

Programs

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] <= c[2] && c[0] <= 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 *)

Extensions

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