A067592 Number of partitions of n into Lucas parts (A000204(k) for k >= 1).

1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 10, 13, 15, 17, 21, 25, 28, 32, 39, 44, 49, 57, 66, 73, 82, 94, 105, 116, 130, 147, 162, 178, 199, 221, 241, 265, 295, 322, 350, 385, 423, 458, 498, 545, 592, 639, 693, 755, 814, 876, 949, 1026, 1100, 1183, 1278, 1371, 1467, 1576, 1694, 1809, 1933, 2072, 2215, 2359, 2517, 2691

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

Sequence in context: A301277 A029033 A041003 * A101195 A036018 A123552

Adjacent sequences: A067589 A067590 A067591 * A067593 A067594 A067595

Keyword

easy,nonn

Author

Naohiro Nomoto, Jan 31 2002

Status

approved