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A067593 Number of partitions of n into Lucas parts (A000032). 3
1, 1, 2, 3, 5, 6, 9, 12, 16, 20, 26, 33, 41, 50, 62, 75, 90, 107, 129, 151, 178, 208, 244, 281, 326, 375, 431, 491, 561, 638, 723, 816, 922, 1037, 1163, 1302, 1458, 1624, 1808, 2009, 2231, 2467, 2729, 3012, 3321, 3651, 4014, 4406, 4828, 5282, 5777, 6308, 6877, 7491, 8155, 8862, 9622, 10438, 11316, 12247, 13249 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/((1-x^2)*prod(i>=1, 1-x^(fibonacci(i-1)+fibonacci(i+1)) ) ). - Emeric Deutsch, Mar 23 2005

G.f.: prod(n>=0, 1 - q^A000032(n) ). [Joerg Arndt, Mar 26 2014]

EXAMPLE

a(5)=6 because we have 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1 and 1+1+1+1+1.

PROG

(PARI) N=66; q='q+O('q^N);

L(n) = fibonacci(n+1) + fibonacci(n-1);

gf = 1; k=0; while( L(k) <= N, gf*=(1-q^L(k)); k+=1 ); gf = 1/gf;

Vec( gf ) /* Joerg Arndt, Mar 26 2014 */

CROSSREFS

Sequence in context: A212864 A026317 A008768 * A084993 A046966 A225973

Adjacent sequences:  A067590 A067591 A067592 * A067594 A067595 A067596

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Jan 31 2002

STATUS

approved

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Last modified November 18 14:15 EST 2017. Contains 294893 sequences.