%I #10 Oct 10 2024 15:15:31

%S 1,1,1,1,2,3,4,4,5,7,11,13,15,17,23,34,40,44,52,67,98,111,124,143,184,

%T 257,290,321,372,467,640,715,793,911,1133,1509,1684,1860,2134,2617,

%U 3424,3801,4202,4796,5828,7484,8292,9148,10419,12532,15872,17529,19332

%N Number of partitions satisfying (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: (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[2] == c[3] && 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, 1, 45}] (* _Jean-François Alcover_, Oct 10 2024 *)

%K nonn

%O 0,5

%A _Olivier Gérard_

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