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

Author

Naohiro Nomoto, Jan 31 2002

Keywords

• easy
• nonn
• look

Links

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

Crossrefs

Cf. A000032, A000119.

Programs

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 *)

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

Formula

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

Extensions

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