A357717 Number of ways to write n as an ordered sum of nine positive Fibonacci numbers (with a single type of 1).

1, 9, 45, 156, 423, 954, 1878, 3321, 5409, 8251, 11979, 16686, 22446, 29250, 37134, 46107, 56259, 67671, 80407, 94338, 109269, 125118, 141930, 159723, 178608, 198522, 219510, 241338, 264438, 288810, 314550, 341010, 367785, 394596, 421443, 448650, 476614, 505404, 534978

Offset: 9

Author

Ilya Gutkovskiy, Oct 10 2022

Keywords

• nonn

Crossrefs

Cf. A000045, A076739, A121548, A121549, A121550, A319402, A357688, A357690, A357691, A357694, A357716.

Programs

Mathematica

nmax = 47; CoefficientList[Series[Sum[x^Fibonacci[k], {k, 2, 21}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

Formula

G.f.: ( Sum_{k>=2} x^Fibonacci(k) )^9.

a(n) = A121548(n,9).