A036824 - OEIS

%I #16 Oct 11 2024 06:56:01

%S 1,0,1,1,1,1,2,2,3,3,4,4,6,6,8,10,11,13,16,17,26,24,32,36,42,60,57,74,

%T 86,93,141,127,171,193,213,306,289,373,428,465,655,623,802,906,995,

%U 1348,1320,1652,1877,2050,2723,2696,3334,3761,4131,5355,5380,6543,7381,8087,10353,10447,12598,14150,15520,19596

%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).

%H Alois P. Heinz, <a href="/A036824/b036824.txt">Table of n, a(n) for n = 0..100</a>

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

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

%t    c[0] == c[1] == c[4] && 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, 0, 54}] (* _Jean-François Alcover_, Oct 11 2024 *)

%K nonn

%O 0,7

%A _Olivier Gérard_

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