A288039 Number of compositions (ordered partitions) of n into Lucas numbers (beginning with 1) (A000204).

1, 1, 1, 2, 4, 6, 9, 16, 27, 43, 70, 118, 195, 318, 524, 868, 1430, 2351, 3878, 6399, 10542, 17367, 28634, 47206, 77793, 128212, 211346, 348360, 574153, 946342, 1559849, 2571016, 4237616, 6984659, 11512526, 18975464, 31276187, 51550993, 84968944, 140049801, 230836734, 380476447, 627119783, 1033648857

Offset

0,4

Links

Table of n, a(n) for n=0..43.

Eric Weisstein's World of Mathematics, Lucas Number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A000204(k)).

Example

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

Mathematica

CoefficientList[Series[1/(1 - Sum[x^LucasL[k], {k, 1, 15}]), {x, 0, 43}], x]

Crossrefs

Cf. A000204, A003263, A067592, A076739, A080888.

Sequence in context: A173241 A096398 A110538 * A373639 A327744 A342340

Adjacent sequences: A288036 A288037 A288038 * A288040 A288041 A288042

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 04 2017

Status

approved