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

0,4

Links

Table of n, a(n) for n=0..71.

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 *)

Crossrefs

Trisection gives: A035592.

Sequence in context: A364790 A094785 A265856 * A205974 A098643 A193474

Adjacent sequences: A035533 A035534 A035535 * A035537 A035538 A035539

Keyword

nonn

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

Status

approved