A103197 Number of compositions of n into Fibonacci number of parts.
1, 2, 4, 7, 12, 21, 37, 65, 115, 208, 386, 727, 1367, 2536, 4630, 8376, 15217, 28170, 53620, 104843, 208547, 416448, 824990, 1608138, 3071813, 5747106, 10561032, 19177849, 34734782, 63495907, 118601911, 228454377, 454988025, 932297291
Offset: 1
Programs
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Mathematica
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 *)
Formula
a(n) = Sum_{k=0..n} binomial(n-1, k-1)*A010056(k).
a(n) = Sum_{k>1} (x/(1-x))^Fibonacci(k).