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

0,4

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: A359946 A328654 A035552 * A352111 A352112 A114862

Adjacent sequences: A339369 A339370 A339371 * A339373 A339374 A339375

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved