A245037 Number of partitions of n where the minimal multiplicity of any part is 6.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 4, 2, 3, 3, 3, 2, 7, 3, 5, 5, 6, 3, 11, 5, 10, 9, 12, 10, 21, 13, 20, 19, 26, 21, 38, 26, 38, 37, 45, 39, 66, 50, 64, 63, 77, 67, 104, 83, 110, 102, 124, 112, 166, 138, 176, 174, 204, 189, 264, 230, 288

Offset

6,13

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..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, 6) -b(n$2, 7):
seq(a(n), n=6..100);

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, 6] - b[n, n, 7];
Table[a[n], {n, 6, 100}] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Column k=6 of A243978.

Sequence in context: A284974 A293222 A305008 * A161311 A161245 A161030

Adjacent sequences: A245034 A245035 A245036 * A245038 A245039 A245040

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Status

approved