A319402 Number of partitions of n into exactly nine positive Fibonacci numbers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 13, 14, 18, 18, 22, 23, 27, 26, 31, 30, 36, 36, 39, 39, 45, 43, 49, 49, 55, 52, 58, 56, 63, 62, 65, 64, 71, 68, 73, 72, 79, 77, 82, 81, 87, 86, 90, 89, 96, 93, 96, 96, 101, 100, 101, 100, 107, 103, 108

Offset: 0

Author

Alois P. Heinz, Sep 18 2018

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..17711

Crossrefs

Column k=9 of A319394.

Cf. A000045.

Programs

Maple

h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
      issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
    end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1 or
      t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
    end:
a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(9):
seq(a(n), n=0..120);

Formula

a(n) = [x^n y^9] 1/Product_{j>=2} (1-y*x^A000045(j)).