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

%I A319503 #24 Dec 08 2020 08:36:47
%S A319503 1,1,0,0,0,1,2,6,16,43,117,305,769,1907,4686,11587,28580,70451,172880,
%T A319503 423629,1036332,2533559,6186635,15092985,36784586,89590410,218069921,
%U A319503 530551804,1290218120,3136385254,7621522229,18515039477,44966884766,109184448962
%N A319503 Number of partitions of Fibonacci(n) into exactly n positive Fibonacci numbers.
%H A319503 Alois P. Heinz, <a href="/A319503/b319503.txt">Table of n, a(n) for n = 0..200</a>
%F A319503 a(n) = [x^A000045(n) y^n] 1/Product_{j>=2} (1-y*x^A000045(j)).
%F A319503 a(n) = A319394(A000045(n),n).
%e A319503 a(0) = 1: the empty partition.
%e A319503 a(1) = 1: 1.
%e A319503 a(5) = 1: 11111.
%e A319503 a(6) = 2: 221111, 311111.
%e A319503 a(7) = 6: 2222221, 3222211, 3322111, 3331111, 5221111, 5311111.
%t A319503 (* Program not suitable for a large number of terms. *)
%t A319503 a[n_] := a[n] = If[n < 2, 1, IntegerPartitions[Fibonacci[n], {n}, Fibonacci[Range[2, n - 1]]] //Length];
%t A319503 Table[Print[n, " ", a[n]]; a[n], {n, 0, 24}] (* _Jean-François Alcover_, Dec 08 2020 *)
%Y A319503 Cf. A000045, A098641, A259254, A319394, A319435.
%K A319503 nonn
%O A319503 0,7
%A A319503 _Alois P. Heinz_, Sep 20 2018