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%I #13 Apr 15 2015 10:09:51
%S 0,1,2,3,5,6,11,15,22,30,40,56,77,101,135,173,231,297,385,490,622,792,
%T 1002,1255,1575,1951,2436,3010,3718,4565,5593,6842,8349,10143,12310,
%U 14868,17977,21637,26015,31185,37316,44583,53174,63261,75175,89104,105558
%N Number of partitions satisfying 0 < cn(1,5) + 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 + 4 + 2 + 3 (OMAABBpp).
%H Alois P. Heinz, <a href="/A039896/b039896.txt">Table of n, a(n) for n = 0..1000</a>
%p b:= proc(n, i, t) option remember; `if`(n=0, t,
%p `if`(i<1, 0, b(n, i-1, t)+ `if`(i>n, 0,
%p b(n-i, i, `if`(irem(i, 5)=0, t, 1)))))
%p end:
%p a:= n-> b(n$2, 0):
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 04 2014
%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, If[Mod[i, 5] == 0, t, 1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Apr 15 2015, after _Alois P. Heinz_ *)
%K nonn
%O 0,3
%A _Olivier Gérard_
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