%I #7 Dec 01 2017 19:00:16
%S 1,2,5,10,18,32,53,84,132,198,294,426,606,852,1178,1610,2178,2910,
%T 3859,5066,6598,8534,10951,13968,17705,22304,27959,34852,43239,53402,
%U 65649,80384,98025,119078,144149,173866,209033,250510,299283,356532,423508
%N Number of partitions of n into Fibonacci parts if each part is of two kinds.
%C Euler transform of 2 x the characteristic function of the Fibonacci numbers.
%H Robert Israel, <a href="/A103577/b103577.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.=1/product((1-x^fibonacci(i))^2, i=2..infinity).
%e a(3)=10 because we have 3, 3', 2+1, 2+1', 2'+1, 2'+1', 1+1+1, 1+1+1', 1+1'+1' and 1'+1'+1'.
%p N:= 12: # to get a(0)..a(M-1) where M = Fibonacci(N-1).
%p G:= mul(1/(1-x^combinat:-fibonacci(i))^2,i=2..N-1):
%p S:= series(G,x,combinat:-fibonacci(N)):
%p seq(coeff(S,x,j),j=0..combinat:-fibonacci(N)-1); # _Robert Israel_, Dec 01 2017
%Y Cf. A003107, A000045.
%K nonn
%O 0,2
%A _Emeric Deutsch_, Mar 23 2005