A319403 Number of partitions of n into exactly ten positive Fibonacci numbers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 14, 15, 19, 20, 24, 25, 31, 30, 35, 36, 42, 42, 48, 47, 54, 54, 59, 60, 69, 66, 73, 72, 80, 79, 86, 85, 92, 91, 97, 96, 107, 103, 110, 110, 118, 117, 123, 123, 132, 130, 135, 134, 142, 141, 146, 145

Offset

0,13

Links

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

Formula

a(n) = [x^n y^10] 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))(10):
seq(a(n), n=0..120);

Crossrefs

Column k=10 of A319394.

Cf. A000045.

Sequence in context: A319401 A322369 A319402 * A029008 A240844 A136343

Adjacent sequences: A319400 A319401 A319402 * A319404 A319405 A319406

Keyword

nonn,look

Author

Alois P. Heinz, Sep 18 2018

Status

approved