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Number of partitions of n into Fibonacci parts if each part is of two kinds.
1

%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