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%I #12 Nov 12 2015 06:06:09
%S 0,0,1,2,3,5,8,12,18,25,37,49,68,91,123,165,215,278,362,465,603,760,
%T 962,1209,1524,1911,2374,2934,3629,4471,5514,6728,8208,9982,12139,
%U 14720,17772,21390,25732,30889,37049,44231,52749,62782,74671,88640
%N Number of partitions satisfying 0 < cn(1,5) + cn(2,5) + cn(3,5) and 0 < cn(4,5) + cn(2,5) + cn(3,5).
%C For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C Short: o < 1 + 2 + 3 and o < 4 + 2 + 3 (OMAABBp).
%H Alois P. Heinz, <a href="/A039901/b039901.txt">Table of n, a(n) for n = 0..1000</a>
%p b:= proc(n, i, t, s) option remember; `if`(n=0, t*s,
%p `if`(i<1, 0, b(n, i-1, t, s)+ `if`(i>n, 0,
%p b(n-i, i, `if`(irem(i, 5) in {0, 4}, t, 1),
%p `if`(irem(i, 5) in {0, 1}, s, 1)))))
%p end:
%p a:= n-> b(n$2, 0$2):
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 03 2014
%t b[n_, i_, t_, s_] := b[n, i, t, s] = If[n == 0, t*s, If[i<1, 0, b[n, i-1, t, s] + If[i>n, 0, b[n-i, i, If[MemberQ[{0, 4}, Mod[i, 5]], t, 1], If[MemberQ[{0, 1}, Mod[i, 5]], s, 1]]]]]; a[n_] := b[n, n, 0, 0]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Nov 12 2015, after _Alois P. Heinz_ *)
%K nonn
%O 0,4
%A _Olivier Gérard_
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