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A290327
Total number of parts in all partitions of n into distinct Lucas numbers (beginning with 1) (A000204).
0
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, 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, 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
OFFSET
1,4
FORMULA
G.f.: Sum_{i>=1} x^A000204(i)/(1 + x^A000204(i))*Product_{j>=1} (1 + x^A000204(j)).
EXAMPLE
a(8) = 5 because we have [7, 1], [4, 3, 1] and 2 + 3 = 5.
MATHEMATICA
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]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 27 2017
STATUS
approved