A294204 - OEIS

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A294204

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

2

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

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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