OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/Product_{n>=1} (1 - q^A000204(n)). - Joerg Arndt, Mar 26 2014
EXAMPLE
a(7) counts these partitions: 7, 43, 4111, 331, 31111, 1111111. - Clark Kimberling, Mar 08 2014
MATHEMATICA
p[n_] := IntegerPartitions[n, All, LucasL@Range@15]; Table[p[n], {n, 0, 12}] (* shows partitions *)
a[n_] := Length@p@n; a /@ Range[0, 80] (* counts partitions, A067592 *)
(* Clark Kimberling, Mar 08 2014 *)
Table[SeriesCoefficient[gf = 1; k = 1; While[LucasL[k] <= n, gf = gf*(1 - x^LucasL[k]); k++]; gf = 1/gf, {x, 0, n}], {n, 0, 100}] (* Vaclav Kotesovec, Mar 26 2014, after Joerg Arndt *)
PROG
(PARI) N=66; q='q+O('q^N);
L(n) = fibonacci(n+2) - fibonacci(n-2);
gf = 1; k=1; while( L(k) <= N, gf*=(1-q^L(k)); k+=1 ); gf = 1/gf;
Vec( gf ) /* Joerg Arndt, Mar 26 2014 */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 31 2002
STATUS
approved