A319503 - OEIS

%I #24 Dec 08 2020 08:36:47

%S 1,1,0,0,0,1,2,6,16,43,117,305,769,1907,4686,11587,28580,70451,172880,

%T 423629,1036332,2533559,6186635,15092985,36784586,89590410,218069921,

%U 530551804,1290218120,3136385254,7621522229,18515039477,44966884766,109184448962

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

%H Alois P. Heinz, <a href="/A319503/b319503.txt">Table of n, a(n) for n = 0..200</a>

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

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

%e a(0) = 1: the empty partition.

%e a(1) = 1: 1.

%e a(5) = 1: 11111.

%e a(6) = 2: 221111, 311111.

%e a(7) = 6: 2222221, 3222211, 3322111, 3331111, 5221111, 5311111.

%t (* Program not suitable for a large number of terms. *)

%t a[n_] := a[n] = If[n < 2, 1, IntegerPartitions[Fibonacci[n], {n}, Fibonacci[Range[2, n - 1]]] //Length];

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 24}] (* _Jean-François Alcover_, Dec 08 2020 *)

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

%K nonn

%O 0,7

%A _Alois P. Heinz_, Sep 20 2018