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%I #5 Jul 27 2017 13:59:56
%S 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 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 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 Total number of parts in all partitions of n into distinct Lucas numbers (beginning with 1) (A000204).
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Sum_{i>=1} x^A000204(i)/(1 + x^A000204(i))*Product_{j>=1} (1 + x^A000204(j)).
%e a(8) = 5 because we have [7, 1], [4, 3, 1] and 2 + 3 = 5.
%t 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 Cf. A000204, A003263, A240225.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Jul 27 2017
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