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

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for related partition-counting sequences

Formula

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

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

Example

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].

Mathematica

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

Crossrefs

Cf. A000204, A003263, A067592, A098641.

Sequence in context: A065845 A137273 A135967 * A146000 A134737 A030733

Adjacent sequences: A290245 A290246 A290247 * A290249 A290250 A290251

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 24 2017

Status

approved