A035534 Number of partitions of n with equal number of parts congruent to each of 0 and 1 (mod 3).

1, 0, 1, 0, 2, 1, 2, 3, 4, 4, 8, 7, 12, 13, 19, 22, 30, 35, 47, 54, 74, 85, 109, 131, 165, 194, 247, 289, 359, 427, 523, 617, 757, 889, 1078, 1272, 1529, 1799, 2154, 2529, 3013, 3528, 4187, 4894, 5779, 6748, 7937, 9241, 10844, 12599, 14724, 17089, 19912, 23048, 26801

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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)+
      `if`(i>n, 0, b(n-i, i, c+irem(i+2, 3)-1))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..70);  # Alois P. Heinz, Dec 07 2016

Mathematica

equalQ[partit_] := Total[Switch[Mod[#, 3], 0, -1, 1, 1, 2, 0]& /@ partit] == 0; a[n_] := Select[IntegerPartitions[n], equalQ] // Length; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 54}] (* Jean-François Alcover, Dec 07 2016 *)

Crossrefs

Sequence in context: A026833 A281544 A056882 * A241416 A082854 A086742

Adjacent sequences: A035531 A035532 A035533 * A035535 A035536 A035537

Keyword

nonn

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

Status

approved