A245040 Number of partitions of n where the minimal multiplicity of any part is 9.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 3, 2, 4, 2, 3, 3, 3, 2, 7, 3, 5, 5, 6, 3, 7, 3, 6, 9, 7, 7, 12, 10, 12, 13, 14, 14, 22, 18, 22, 24, 26, 25, 35, 28, 34, 40, 42, 41, 52, 46, 55, 59, 64, 58, 81, 70, 82, 85, 92

Offset

9,19

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 9..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, 9) -b(n$2, 10):
seq(a(n), n=9..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, 9] - b[n, n, 10];
Table[a[n], {n, 9, 100}] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Column k=9 of A243978.

Sequence in context: A076622 A194513 A344018 * A161314 A161248 A161033

Adjacent sequences: A245037 A245038 A245039 * A245041 A245042 A245043

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Status

approved