A319400 Number of partitions of n into exactly seven positive Fibonacci numbers.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 9, 9, 11, 11, 14, 14, 16, 15, 19, 17, 20, 20, 22, 21, 24, 22, 27, 25, 27, 26, 31, 28, 30, 29, 32, 29, 32, 30, 34, 33, 34, 34, 37, 36, 38, 36, 41, 37, 38, 39, 41, 41, 40, 39, 41, 38, 41, 38, 41, 42, 40, 41, 46, 43

Offset

0,10

Links

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

Formula

a(n) = [x^n y^7] 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))(7):
seq(a(n), n=0..120);

Crossrefs

Column k=7 of A319394.

Cf. A000045.

Sequence in context: A348588 A106247 A337030 * A174787 A094909 A237799

Adjacent sequences: A319397 A319398 A319399 * A319401 A319402 A319403

Keyword

nonn,look

Author

Alois P. Heinz, Sep 18 2018

Status

approved