A067593 Number of partitions of n into Lucas parts (A000032).

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

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.: 1 / 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: A026317 A361848 A008768 * A084993 A046966 A225973

Adjacent sequences: A067590 A067591 A067592 * A067594 A067595 A067596

Keyword

easy,nonn

Author

Naohiro Nomoto, Jan 31 2002

Status

approved