%I #10 Oct 11 2024 06:56:20

%S 1,1,1,1,2,2,3,3,4,5,7,8,10,11,14,21,24,26,31,39,60,65,72,82,107,155,

%T 170,185,214,271,383,419,459,525,660,896,987,1078,1234,1524,2024,2221,

%U 2437,2775,3391,4403,4832,5296,6024,7271,9304,10180,11168,12650,15146

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

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

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

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

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

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

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 54}] (* _Jean-François Alcover_, Oct 11 2024 *)

%K nonn

%O 0,5

%A _Olivier Gérard_

%E a(0)=1 prepended by _Jean-François Alcover_, Oct 11 2024