A308062 Number of ordered factorizations of n into Fibonacci numbers > 1.

1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 0, 3, 1, 0, 2, 3, 0, 3, 0, 3, 1, 0, 0, 6, 1, 2, 1, 0, 0, 6, 0, 4, 0, 1, 0, 6, 0, 0, 2, 6, 0, 2, 0, 0, 3, 0, 0, 11, 0, 3, 0, 3, 0, 4, 1, 0, 0, 0, 0, 12, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 0, 13, 0, 0, 3, 0, 0, 6, 0, 11, 1, 0, 0, 3, 0, 0, 0, 0, 1, 12

Offset: 1

Author

Ilya Gutkovskiy, May 10 2019

Keywords

• nonn

Crossrefs

Cf. A000045, A010056, A065105 (positions of zeros), A065108 (positions of nonzero terms), A074206.

Programs

Mathematica

terms = 90; A[] = 0; Do[A[x] = x + Sum[A[x^Fibonacci[k]], {k, 3, 25}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
f[n_] := f[n] = SeriesCoefficient[Sum[x^Fibonacci[k], {k, 3, 25}], {x, 0, n}]; a[n_] := If[n == 1, n, Sum[If[d < n, f[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 90}]

Formula

G.f. A(x) satisfies: A(x) = x + Sum_{k>=3} A(x^Fibonacci(k)).