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A339371 Number of partitions of n into an even number of Fibonacci parts (with a single type of 1). 1
1, 0, 1, 1, 3, 2, 5, 4, 8, 7, 13, 12, 18, 18, 27, 27, 39, 38, 53, 53, 72, 73, 96, 98, 126, 128, 165, 168, 209, 216, 266, 274, 334, 345, 416, 430, 514, 533, 628, 655, 766, 797, 929, 966, 1115, 1164, 1336, 1395, 1590, 1661, 1885, 1969, 2226, 2326, 2611, 2734 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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(7) = 4 because we have [5, 2], [3, 2, 1, 1], [2, 2, 2, 1] and [2, 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, A027187, A093997, A093998, A298949, A339372.

Sequence in context: A318460 A276582 A240729 * A258259 A240182 A115297

Adjacent sequences:  A339368 A339369 A339370 * A339372 A339373 A339374

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 02 2020

STATUS

approved

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)