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

0,8

Comments

Convolution of the sequences A067595 and A033999.

Links

Table of n, a(n) for n=0..100.

Ilya Gutkovskiy, Extended graphical example

Index entries for sequences related to partitions

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A025822 A051585 A049115 * A329697 A029367 A192541

Adjacent sequences: A294201 A294202 A294203 * A294205 A294206 A294207

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 24 2017

Status

approved