A280168 Expansion of Product_{k>=2} 1/(1 - x^(Fibonacci(k)^2)).

1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 41, 43, 45, 48, 50, 52, 54, 57, 60, 62, 65, 68, 72, 74, 77, 80, 84, 87, 90, 94, 98, 102, 106, 110, 114, 118, 123, 127, 132, 136, 142, 147, 152, 157, 163, 169, 174, 180, 186, 193, 199

Offset: 0

Author

Ilya Gutkovskiy, Dec 27 2016

Keywords

• nonn

Comments

Number of partitions of n into squares of Fibonacci numbers (with a single type of 1).

Examples

			a(8) = 3 because we have [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
		

Links

• Index entries for sequences related to sums of squares
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000119, A000121, A001156, A003107, A007000, A007598, A238999, A239002.

Programs

Mathematica

CoefficientList[Series[Product[1/(1 - x^Fibonacci[k]^2), {k, 2, 20}], {x, 0, 82}], x]

Formula

G.f.: Product_{k>=2} 1/(1 - x^(Fibonacci(k)^2)).