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

0,12

Links

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

Formula

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

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);

Crossrefs

Column k=9 of A319394.

Cf. A000045.

Sequence in context: A318029 A319401 A322369 * A319403 A029008 A240844

Adjacent sequences: A319399 A319400 A319401 * A319403 A319404 A319405

Keyword

nonn,look

Author

Alois P. Heinz, Sep 18 2018

Status

approved