%I #22 Feb 02 2020 07:53:52

%S 1,1,2,3,5,6,9,12,16,20,26,33,41,50,62,75,90,107,129,151,178,208,244,

%T 281,326,375,431,491,561,638,723,816,922,1037,1163,1302,1458,1624,

%U 1808,2009,2231,2467,2729,3012,3321,3651,4014,4406,4828,5282,5777,6308,6877,7491,8155,8862,9622,10438,11316,12247,13249

%N Number of partitions of n into Lucas parts (A000032).

%H Seiichi Manyama, <a href="/A067593/b067593.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1/((1-x^2)*prod(i>=1, 1-x^(fibonacci(i-1)+fibonacci(i+1)) ) ). - _Emeric Deutsch_, Mar 23 2005

%F G.f.: 1 / prod(n>=0, 1 - q^A000032(n) ). [_Joerg Arndt_, Mar 26 2014]

%e 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.

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

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

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

%o Vec( gf ) /* _Joerg Arndt_, Mar 26 2014 */

%K easy,nonn

%O 0,3

%A _Naohiro Nomoto_, Jan 31 2002