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

0,11

Links

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

Formula

a(n) = [x^n y^8] 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))(8):
seq(a(n), n=0..120);

Crossrefs

Column k=8 of A319394.

Cf. A000045.

Sequence in context: A094909 A237799 A318029 * A322369 A319402 A319403

Adjacent sequences: A319398 A319399 A319400 * A319402 A319403 A319404

Keyword

nonn,look

Author

Alois P. Heinz, Sep 18 2018

Status

approved