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A067595 Number of partitions of n into distinct Lucas parts (A000032). 24
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Sequence in context: A266547 A127992 A169989 * A184721 A134868 A237259

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

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Last modified September 23 17:50 EDT 2017. Contains 292363 sequences.