A244516 Number of partitions of n where the minimal multiplicity of any part is 3.

0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 2, 3, 3, 2, 7, 3, 5, 9, 8, 7, 16, 12, 17, 23, 23, 25, 42, 33, 43, 59, 61, 59, 95, 85, 104, 128, 137, 148, 207, 189, 233, 283, 307, 320, 430, 424, 498, 584, 634, 686, 872, 864, 1011, 1177, 1280, 1365, 1687, 1736, 1987, 2258, 2470, 2674, 3208, 3303, 3767, 4277, 4658, 5014, 5916, 6201

Offset

1,9

Comments

Column k=3 of A243978.

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))
    end:
a:= n-> b(n$2, 3) -b(n$2, 4):
seq(a(n), n=1..80);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + Sum[b[n - i*j, i - 1, k], {j, Max[1, k], n/i}]]];
a[n_] := b[n, n, 3] - b[n, n, 4];
Array[a, 80] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Sequence in context: A340828 A123265 A104345 * A363264 A002339 A123243

Adjacent sequences: A244513 A244514 A244515 * A244517 A244518 A244519

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved