A319503 Number of partitions of Fibonacci(n) into exactly n positive Fibonacci numbers.

1, 1, 0, 0, 0, 1, 2, 6, 16, 43, 117, 305, 769, 1907, 4686, 11587, 28580, 70451, 172880, 423629, 1036332, 2533559, 6186635, 15092985, 36784586, 89590410, 218069921, 530551804, 1290218120, 3136385254, 7621522229, 18515039477, 44966884766, 109184448962

Offset: 0

Author

Alois P. Heinz, Sep 20 2018

Keywords

• nonn

Examples

			a(0) = 1: the empty partition.
a(1) = 1: 1.
a(5) = 1: 11111.
a(6) = 2: 221111, 311111.
a(7) = 6: 2222221, 3222211, 3322111, 3331111, 5221111, 5311111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000045, A098641, A259254, A319394, A319435.

Programs

Mathematica

(* Program not suitable for a large number of terms. *)
a[n_] := a[n] = If[n < 2, 1, IntegerPartitions[Fibonacci[n], {n}, Fibonacci[Range[2, n - 1]]] //Length];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 24}] (* Jean-François Alcover, Dec 08 2020 *)

Formula

a(n) = [x^A000045(n) y^n] 1/Product_{j>=2} (1-y*x^A000045(j)).

a(n) = A319394(A000045(n),n).