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 A290327 #5 Jul 27 2017 13:59:56
%S A290327 1,0,1,3,2,0,3,5,0,2,6,5,0,5,9,3,0,6,9,0,5,12,7,0,9,12,0,3,10,9,0,9,
%T A290327 17,7,0,12,16,0,7,18,12,0,12,18,4,0,10,14,0,9,21,12,0,17,22,0,7,21,16,
%U A290327 0,16,27,9,0,18,23,0,12,27,15,0,18,22,0,4,15,14,0,14,27,12,0,21,27,0,12,32,22,0,22
%N A290327 Total number of parts in all partitions of n into distinct Lucas numbers (beginning with 1) (A000204).
%H A290327 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A290327 G.f.: Sum_{i>=1} x^A000204(i)/(1 + x^A000204(i))*Product_{j>=1} (1 + x^A000204(j)).
%e A290327 a(8) = 5 because we have [7, 1], [4, 3, 1] and 2 + 3 = 5.
%t A290327 nmax = 90; Rest[CoefficientList[Series[Sum[x^LucasL[i]/(1 + x^LucasL[i]) Product[(1 + x^LucasL[j]), {j, 1, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]
%Y A290327 Cf. A000204, A003263, A240225.
%K A290327 nonn
%O A290327 1,4
%A A290327 _Ilya Gutkovskiy_, Jul 27 2017