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A339372 Number of partitions of n into an odd number of Fibonacci parts (with a single type of 1). 1

%I

%S 0,1,1,2,1,4,3,6,6,10,9,15,15,23,22,32,32,45,46,62,62,84,84,110,113,

%T 144,147,185,191,237,243,299,308,372,387,462,479,569,591,695,723,843,

%U 879,1017,1063,1222,1273,1459,1523,1732,1812,2048,2141,2411,2523,2830

%N Number of partitions of n into an odd number of Fibonacci parts (with a single type of 1).

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

%F a(n) = (A003107(n) - A298949(n)) / 2.

%e a(8) = 6 because we have [8], [5, 2, 1], [3, 3, 2], [3, 2, 1, 1, 1], [2, 2, 2, 1, 1] and [2, 1, 1, 1, 1, 1, 1].

%t nmax = 55; CoefficientList[Series[(1/2) (Product[1/(1 - x^Fibonacci[k]), {k, 2, 26}] - Product[1/(1 + x^Fibonacci[k]), {k, 2, 26}]), {x, 0, nmax}], x]

%Y Cf. A000045, A003107, A027193, A093997, A093998, A298949, A339371.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Dec 02 2020

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Last modified August 2 02:10 EDT 2021. Contains 346408 sequences. (Running on oeis4.)