A319399 Number of partitions of n into exactly six positive Fibonacci numbers.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 9, 9, 12, 10, 12, 12, 14, 13, 15, 13, 16, 15, 16, 15, 19, 16, 18, 18, 20, 18, 20, 17, 20, 17, 19, 19, 21, 21, 20, 20, 24, 21, 23, 21, 23, 22, 22, 23, 24, 23, 23, 20, 22, 21, 20, 21, 24, 22, 22, 23, 25, 25, 27, 23

Offset

0,9

Links

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

Formula

a(n) = [x^n y^6] 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))(6):
seq(a(n), n=0..120);

Crossrefs

Column k=6 of A319394.

Cf. A000045.

Sequence in context: A239933 A061106 A352928 * A352434 A161764 A293706

Adjacent sequences: A319396 A319397 A319398 * A319400 A319401 A319402

Keyword

nonn,look

Author

Alois P. Heinz, Sep 18 2018

Status

approved