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

Author

Ilya Gutkovskiy, Jun 04 2017

Keywords

• nonn

Examples

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

Links

• Eric Weisstein's World of Mathematics, Lucas Number
• Index entries for sequences related to compositions

Crossrefs

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

Programs

Mathematica

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

Formula

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