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

Author

Ilya Gutkovskiy, Aug 28 2017

Keywords

• nonn

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, ...).

Examples

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

Links

• Index entries for related partition-counting sequences

Crossrefs

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

Programs

Mathematica

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

Formula

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