A290327 Total number of parts in all partitions of n into distinct Lucas numbers (beginning with 1) (A000204).

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

Author

Ilya Gutkovskiy, Jul 27 2017

Keywords

• nonn

Examples

			a(8) = 5 because we have [7, 1], [4, 3, 1] and 2 + 3 = 5.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000204, A003263, A240225.

Programs

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]]

Formula

G.f.: Sum_{i>=1} x^A000204(i)/(1 + x^A000204(i))*Product_{j>=1} (1 + x^A000204(j)).