A291650 Expansion of Product_{k>=2} (1 + x^Fibonacci(k))^Fibonacci(k).

1, 1, 2, 5, 4, 12, 14, 16, 42, 35, 65, 100, 84, 205, 201, 254, 490, 386, 749, 917, 851, 1816, 1566, 2260, 3513, 2784, 5566, 5748, 6116, 11366, 9048, 14740, 19037, 16095, 31576, 28505, 35218, 56334, 43671, 77512, 85163, 80577, 147756, 121016, 172408, 236022

Offset

0,3

Comments

Number of partitions of n into distinct Fibonacci parts (1 counted as single Fibonacci number), where Fibonacci(k) different parts of size Fibonacci(k) are available (1a, 2a, 2b, 3a, 3b, 3c, ...).

Links

Table of n, a(n) for n=0..45.

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=2} (1 + x^A000045(k))^A000045(k).

Example

a(3) = 5 because we have [3a], [3b], [3c], [2a, 1a] and [2b, 1a].

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x^Fibonacci[k])^Fibonacci[k], {k, 2, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000045, A000119, A000121, A026007, A166861, A200544, A239002, A260787, A261050.

Sequence in context: A362418 A329372 A338108 * A285292 A346595 A126356

Adjacent sequences: A291647 A291648 A291649 * A291651 A291652 A291653

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 28 2017

Status

approved