A036811 - OEIS

%I #10 Oct 10 2024 15:15:59

%S 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,

%T 218,237,274,349,495,542,593,679,855,1165,1281,1399,1602,1981,2642,

%U 2893,3172,3613,4420,5770,6313,6913,7862,9505,12234,13345,14619,16558

%N 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)).

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

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

%t okQ[p_] := Module[{c},

%t    c[k_] := c[k] = Count[Mod[p, 5], k];

%t    c[2] == c[3] && c[0] <= c[1] &&

%t    c[0] <= c[4] && c[2] <= c[1] &&

%t    c[2] <= c[4]];

%t a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];

%t Table[Print[n, " ", a[n]]; a[n], {n, 1, 45}] (* _Jean-François Alcover_, Oct 10 2024 *)

%K nonn,changed

%O 0,5

%A _Olivier Gérard_

%E a(0)=1 prepended by _Alois P. Heinz_, Oct 10 2024