login
Number of compositions of n into Fibonacci number of parts.
0

%I #6 May 01 2014 17:03:12

%S 1,2,4,7,12,21,37,65,115,208,386,727,1367,2536,4630,8376,15217,28170,

%T 53620,104843,208547,416448,824990,1608138,3071813,5747106,10561032,

%U 19177849,34734782,63495907,118601911,228454377,454988025,932297291

%N Number of compositions of n into Fibonacci number of parts.

%F a(n) = Sum_{k=0..n} binomial(n-1, k-1)*A010056(k).

%F a(n) = Sum_{k>1} (x/(1-x))^Fibonacci(k).

%t Flatten[{1,2,4,Table[SeriesCoefficient[Sum[(x/(1-x))^Fibonacci[k],{k,2,n}],{x,0,n}],{n,4,35}]}] (* _Vaclav Kotesovec_, May 01 2014 *)

%Y Cf. A102848, A052467.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Mar 18 2005