A339372 Number of partitions of n into an odd number of Fibonacci parts (with a single type of 1).
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, 144, 147, 185, 191, 237, 243, 299, 308, 372, 387, 462, 479, 569, 591, 695, 723, 843, 879, 1017, 1063, 1222, 1273, 1459, 1523, 1732, 1812, 2048, 2141, 2411, 2523, 2830
Offset: 0
Keywords
Examples
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].
Programs
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Mathematica
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]