login
Expansion of Product_{k>=2} 1/(1 - x^(Fibonacci(k)^2)).
1

%I #4 Dec 27 2016 23:22:19

%S 1,1,1,1,2,2,2,2,3,4,4,4,5,6,6,6,7,8,9,9,10,11,12,12,13,15,16,17,18,

%T 20,21,22,23,25,27,28,30,32,34,35,37,39,41,43,45,48,50,52,54,57,60,62,

%U 65,68,72,74,77,80,84,87,90,94,98,102,106,110,114,118,123,127,132,136,142,147,152,157,163,169,174,180,186,193,199

%N Expansion of Product_{k>=2} 1/(1 - x^(Fibonacci(k)^2)).

%C Number of partitions of n into squares of Fibonacci numbers (with a single type of 1).

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=2} 1/(1 - x^(Fibonacci(k)^2)).

%e a(8) = 3 because we have [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].

%t CoefficientList[Series[Product[1/(1 - x^Fibonacci[k]^2), {k, 2, 20}], {x, 0, 82}], x]

%Y Cf. A000119, A000121, A001156, A003107, A007000, A007598, A238999, A239002.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Dec 27 2016