A245038 Number of partitions of n where the minimal multiplicity of any part is 7.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 3, 3, 2, 4, 2, 3, 3, 6, 3, 6, 4, 6, 4, 6, 7, 9, 8, 9, 11, 14, 11, 19, 17, 20, 21, 25, 24, 31, 32, 36, 37, 44, 40, 52, 52, 65, 58, 70, 69, 83, 78, 93, 99, 111, 104, 126, 124, 142, 141, 177, 167, 201

Offset

7,15

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 7..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, 7) -b(n$2, 8):
seq(a(n), n=7..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, 7] - b[n, n, 8];
Table[a[n], {n, 7, 100}] (* Jean-François Alcover, May 01 2018, translated from Maple *)

Crossrefs

Column k=7 of A243978.

Sequence in context: A123738 A194511 A214526 * A161312 A161246 A161031

Adjacent sequences: A245035 A245036 A245037 * A245039 A245040 A245041

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 10 2014

Status

approved