A294204 Number of partitions of n into distinct Lucas parts (A000032) greater than 1.

1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 0, 3, 2, 2, 2, 2, 3, 0, 3, 1, 3, 1, 3, 3, 2, 3, 2, 4, 0, 4, 2, 3, 2, 3, 3, 1, 3, 1, 4, 0, 4, 3, 3, 3, 3, 5, 0, 5, 2, 4, 2, 4, 4, 2, 4, 2, 5, 0, 5, 3, 3, 3, 3, 4, 0, 4, 1, 4, 1, 4, 4, 3, 4, 3, 6, 0, 6, 3, 5, 3, 5, 5, 2, 5, 2, 6, 0, 6, 4, 4, 4, 4

Offset: 0

Author

Ilya Gutkovskiy, Oct 24 2017

Keywords

• nonn

Comments

Convolution of the sequences A067595 and A033999.

Examples

			a(9) = 2 because we have [7, 2] and [4, 3, 2].
		

Links

• Ilya Gutkovskiy, Extended graphical example
• Index entries for sequences related to partitions

Crossrefs

Cf. A000032, A033999, A067593, A067595, A239002, A294203.

Programs

Mathematica

CoefficientList[Series[(1 + x^2) Product[1 + x^LucasL[k], {k, 2, 15}], {x, 0, 100}], x]

Formula

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