A036813 - OEIS

%I #10 Oct 10 2024 15:16:18

%S 1,0,1,1,1,2,2,3,4,4,8,6,11,12,14,23,21,31,37,40,66,59,87,100,113,171,

%T 162,224,261,289,431,408,556,639,714,1017,993,1304,1504,1670,2322,

%U 2288,2958,3384,3768,5089,5099,6447,7372,8181,10836,10949,13654,15537

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

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

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

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

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

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

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

%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

%O 0,6

%A _Olivier Gérard_

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