A035537 Number of partitions of n with equal nonzero number of parts congruent to each of 0 and 1 (mod 3).

0, 0, 0, 0, 1, 0, 1, 2, 2, 3, 5, 5, 9, 10, 15, 18, 24, 30, 40, 47, 65, 76, 97, 120, 150, 179, 229, 270, 336, 404, 494, 588, 722, 852, 1035, 1227, 1476, 1744, 2090, 2461, 2935, 3446, 4092, 4795, 5665, 6627, 7801, 9096, 10680, 12426, 14528, 16881, 19680, 22800, 26525

Offset

0,8

Links

Table of n, a(n) for n=0..54.

Maple

b := proc(n, i, t, s) option remember; `if`(n=0,
  `if`(t = s and t >= 1, 1, 0), `if`(i<1, 0, b(n, i-1, t, s)+
  b(n-i, min(n-i, i), t + [1, 0, 0][1+irem(i, 3)], s + [0, 1, 0][1+irem(i, 3)])))
  end:
seq(b(n, n, 0, 0), n=0..50); # Georg Fischer, Sep 13 2020

Mathematica

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

Crossrefs

Sequence in context: A011971 A060048 A110699 * A285407 A292802 A247376

Adjacent sequences: A035534 A035535 A035536 * A035538 A035539 A035540

Keyword

nonn

Author

Olivier Gérard

Status

approved