A245041 Number of partitions of n where the minimal multiplicity of any part is 10.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 2, 3, 3, 3, 2, 4, 2, 3, 3, 6, 3, 6, 4, 6, 4, 6, 3, 7, 4, 9, 6, 11, 7, 13, 11, 14, 12, 17, 13, 25, 18, 24, 22, 30, 26, 35, 28, 37, 33, 49, 37, 53, 45, 56, 54, 67, 58

Offset

10,21

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 10..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, 10) -b(n$2, 11):
seq(a(n), n=10..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, 10] - b[n, n, 11];
Table[a[n], {n, 10, 100}] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Column k=10 of A243978.

Sequence in context: A185217 A131456 A074944 * A161315 A161249 A161034

Adjacent sequences: A245038 A245039 A245040 * A245042 A245043 A245044

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Status

approved