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

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Keywords

• nonn

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A243978.

Programs

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 *)