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

Author

Naohiro Nomoto, Jan 31 2002

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Programs

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 */

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]