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A067595 Number of partitions of n into distinct Lucas parts (A000032). 27
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

Cf. A000032, A000119.

Sequence in context: A127992 A327390 A169989 * A184721 A134868 A322861

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 May 26 21:56 EDT 2022. Contains 354092 sequences. (Running on oeis4.)