This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288039 #9 Feb 16 2025 08:33:47
%S A288039 1,1,1,2,4,6,9,16,27,43,70,118,195,318,524,868,1430,2351,3878,6399,
%T A288039 10542,17367,28634,47206,77793,128212,211346,348360,574153,946342,
%U A288039 1559849,2571016,4237616,6984659,11512526,18975464,31276187,51550993,84968944,140049801,230836734,380476447,627119783,1033648857
%N A288039 Number of compositions (ordered partitions) of n into Lucas numbers (beginning with 1) (A000204).
%H A288039 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LucasNumber.html">Lucas Number</a>
%H A288039 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A288039 G.f.: 1/(1 - Sum_{k>=1} x^A000204(k)).
%e A288039 a(4) = 4 because we have [4], [3, 1], [1, 3] and [1, 1, 1, 1].
%t A288039 CoefficientList[Series[1/(1 - Sum[x^LucasL[k], {k, 1, 15}]), {x, 0, 43}], x]
%Y A288039 Cf. A000204, A003263, A067592, A076739, A080888.
%K A288039 nonn
%O A288039 0,4
%A A288039 _Ilya Gutkovskiy_, Jun 04 2017