A339371 Number of partitions of n into an even number of Fibonacci parts (with a single type of 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

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 A364311

Adjacent sequences: A339368 A339369 A339370 * A339372 A339373 A339374

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved