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A339372 Number of partitions of n into an odd number of Fibonacci parts (with a single type of 1). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..55.

Index entries for sequences related to partitions

FORMULA

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

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

EXAMPLE

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].

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]

CROSSREFS

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

Sequence in context: A071065 A328654 A035552 * A114862 A064579 A277376

Adjacent sequences:  A339369 A339370 A339371 * A339373 A339374 A339375

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified April 12 09:28 EDT 2021. Contains 342920 sequences. (Running on oeis4.)