A067595 Number of partitions of n into distinct Lucas parts (A000032).

1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 5, 4, 4, 4, 5, 3, 3, 4, 4, 4, 4, 6, 5, 5, 5, 6, 4, 4, 6, 5, 5, 5, 6, 4, 4, 4, 5, 4, 4, 7, 6, 6, 6, 8, 5, 5, 7, 6, 6, 6, 8, 6, 6, 6, 7, 5, 5, 8, 6, 6, 6, 7, 4, 4, 5, 5, 5, 5, 8, 7, 7, 7, 9, 6, 6, 9, 8, 8, 8, 10, 7, 7, 7, 8, 6, 6, 10, 8, 8, 8, 10, 6, 6, 8

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..15127

Formula

G.f.: B(x) * (1 + x^2) where B(x) is the g.f. of A003263. [Joerg Arndt, Jul 14 2013]

Mathematica

n1 = 10; n2 = LucasL[n1]; (1 + x^2)*Product[1 + x^LucasL[n], {n, 1, n1}] + O[x]^n2 // CoefficientList[#, x]& (* Jean-François Alcover, Feb 17 2017, after Joerg Arndt *)

Prog

(PARI)
L(n) = fibonacci(n+1) + fibonacci(n-1);
N = 66;  x = 'x + O('x^N);
gf = prod(n=0, 11, 1 + x^L(n) );
\\gf = prod(n=1, 11, 1 + x^L(n) ) * (1+x^2); \\ same g.f.
Vec(gf) \\ Joerg Arndt, Jul 14 2013

Crossrefs

Cf. A000032, A000119.

Sequence in context: A127992 A327390 A169989 * A184721 A369705 A134868

Adjacent sequences: A067592 A067593 A067594 * A067596 A067597 A067598

Keyword

easy,nonn,look

Author

Naohiro Nomoto, Jan 31 2002

Extensions

Corrected a(0), Joerg Arndt, Jul 14 2013

Status

approved