A319401 Number of partitions of n into exactly eight positive Fibonacci numbers.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 10, 12, 13, 16, 16, 20, 19, 23, 22, 25, 25, 30, 28, 31, 31, 35, 34, 39, 36, 42, 40, 43, 42, 47, 44, 47, 46, 51, 48, 52, 51, 56, 55, 57, 56, 62, 59, 62, 60, 65, 64, 64, 65, 67, 64, 67, 65, 70, 67, 69, 68, 72

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=8 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))(8):
seq(a(n), n=0..120);

Formula

a(n) = [x^n y^8] 1/Product_{j>=2} (1-y*x^A000045(j)).