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%I #8 Dec 07 2016 09:43:49
%S 0,0,0,0,0,1,1,1,3,4,5,8,11,14,19,26,34,43,56,72,90,114,145,178,222,
%T 277,338,414,511,619,751,913,1101,1324,1595,1909,2282,2724,3243,3850,
%U 4569,5406,6387,7530,8869,10423,12231,14332,16775,19591,22864,26643,31000
%N Number of partitions of n with equal nonzero number of parts congruent to each of 0 and 2 (mod 3)
%t equalQ[partit_] := With[{ t = Total[Switch[Mod[#, 3], 0, {1, 0, 0}, 1, {0, 1, 0}, 2, {0, 0, 1}]& /@ partit]}, t[[1]] > 0 && t[[1]] == t[[3]]]; a[n_] := Select[IntegerPartitions[n], equalQ] // Length; a[0] = 0; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 52}] (* _Jean-François Alcover_, Dec 07 2016 *)
%K nonn
%O 0,9
%A _Olivier Gérard_
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