A245039 Number of partitions of n where the minimal multiplicity of any part is 8.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 3, 3, 3, 2, 4, 2, 6, 4, 5, 4, 7, 3, 6, 4, 10, 6, 10, 7, 14, 11, 13, 12, 23, 15, 23, 20, 28, 24, 32, 26, 43, 34, 43, 39, 56, 45, 59, 55, 73, 63, 80, 70, 94, 81, 101, 92, 127, 104, 131

Offset

8,17

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..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, 8) -b(n$2, 9):
seq(a(n), n=8..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, 8] - b[n, n, 9];
Table[a[n], {n, 8, 100}] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Column k=8 of A243978.

Sequence in context: A280986 A344773 A103689 * A161313 A161247 A161032

Adjacent sequences: A245036 A245037 A245038 * A245040 A245041 A245042

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Status

approved