A035535 Number of partitions of n with equal number of parts congruent to each of 0 and 2 (mod 3).

1, 1, 1, 1, 2, 3, 3, 4, 7, 8, 10, 14, 18, 22, 29, 37, 47, 58, 73, 91, 113, 140, 174, 211, 260, 319, 386, 468, 572, 687, 828, 998, 1197, 1431, 1714, 2041, 2430, 2887, 3424, 4051, 4792, 5651, 6659, 7829, 9199, 10786, 12631, 14770, 17258, 20120, 23444, 27278

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)+
       b(n-i, min(n-i, i), c+[1, 0, -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, -1, 1, 0, 2, 1]& /@ partit] == 0; a[n_] := Select[IntegerPartitions[n] , equalQ] // Length; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 51}] (* Jean-François Alcover, Dec 07 2016 *)

Crossrefs

Sequence in context: A114863 A152980 A170891 * A154309 A249579 A329301

Adjacent sequences: A035532 A035533 A035534 * A035536 A035537 A035538

Keyword

nonn

Author

Olivier Gérard

Extensions

More terms from David W. Wilson

Status

approved