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A035536 Number of partitions of n with equal number of parts congruent to each of 1 and 2 (mod 3).

%I A035536 #16 Jun 01 2025 22:26:54
%S A035536 1,0,0,2,0,0,6,0,0,14,0,0,32,0,0,66,0,0,134,0,0,256,0,0,480,0,0,868,0,
%T A035536 0,1540,0,0,2664,0,0,4536,0,0,7574,0,0,12474,0,0,20234,0,0,32428,0,0,
%U A035536 51324,0,0,80388,0,0,124582,0,0,191310,0,0,291114,0,0,439394,0,0,657936,0,0
%N A035536 Number of partitions of n with equal number of parts congruent to each of 1 and 2 (mod 3).
%p A035536 b:= proc(n, i, c) option remember; `if`(n=0,
%p A035536       `if`(c=0, 1, 0), `if`(i<1, 0, b(n, i-1, c)+
%p A035536        b(n-i, min(n-i, i), c+[0, 1, -1][1+irem(i, 3)])))
%p A035536     end:
%p A035536 a:= n-> b(n$2, 0):
%p A035536 seq(a(n), n=0..70);  # _Alois P. Heinz_, Sep 04 2020
%t A035536 equalQ[partit_] := Total[Switch[Mod[#, 3], 0, 0, 1, 1, 2, -1]& /@ partit] == 0; a[n_] := If[Mod[n, 3] != 0, 0, Select[IntegerPartitions[n], equalQ] // Length]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 71}] (* _Jean-François Alcover_, Dec 07 2016 *)
%Y A035536 Trisection gives: A035592.
%K A035536 nonn
%O A035536 0,4
%A A035536 _Olivier Gérard_
%E A035536 More terms from _David W. Wilson_