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

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, 0, 1540, 0, 0, 2664, 0, 0, 4536, 0, 0, 7574, 0, 0, 12474, 0, 0, 20234, 0, 0, 32428, 0, 0, 51324, 0, 0, 80388, 0, 0, 124582, 0, 0, 191310, 0, 0, 291114, 0, 0, 439394, 0, 0, 657936, 0, 0

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Crossrefs

Trisection gives: A035592.

Programs

Maple

b:= proc(n, i, c) option remember; `if`(n=0,
      `if`(c=0, 1, 0), `if`(i<1, 0, b(n, i-1, c)+
       b(n-i, min(n-i, i), c+[0, 1, -1][1+irem(i, 3)])))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..70);  # Alois P. Heinz, Sep 04 2020

Mathematica

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 *)

Extensions

More terms from David W. Wilson