A290248 Number of partitions of the n-th Lucas number into Lucas parts (beginning with 1) (A000204).

1, 2, 3, 6, 13, 39, 147, 755, 5230, 50282, 677730, 13010007, 359551127, 14457741910, 853120090801, 74437567936635, 9666377127590346, 1878877762201043122, 549363336929733878734, 242695457366120511255070, 16263199149257162654631846

Offset: 1

Author

Ilya Gutkovskiy, Jul 24 2017

Keywords

• nonn

Examples

			a(4) = 6 because Lucas(4) = 7 and we have [7], [4, 3], [4, 1, 1, 1], [3, 3, 1], [3, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000204, A003263, A067592, A098641.

Programs

Mathematica

Rest[Table[SeriesCoefficient[Product[1/(1 - x^LucasL[k]), {k, 1, n}], {x, 0, LucasL[n]}], {n, 0, 21}]]

Formula

a(n) = [x^A000204(n)] Product_{k>=1} 1/(1 - x^A000204(k)).

a(n) = A067592(A000204(n)).