login
A238999
Number of partitions of n using Fibonacci numbers > 1.
4
1, 0, 1, 1, 1, 2, 2, 2, 4, 3, 5, 5, 6, 8, 8, 10, 12, 12, 16, 16, 19, 23, 23, 28, 31, 33, 40, 41, 47, 53, 56, 64, 69, 75, 86, 89, 101, 109, 117, 131, 139, 151, 168, 175, 195, 208, 223, 245, 259, 280, 304, 320, 350, 370, 397, 430, 452, 488, 521, 550, 596, 626
OFFSET
0,6
LINKS
FORMULA
G.f.: 1/Product_{i>=3} (1 - x^Fibonacci(i)).
EXAMPLE
a(12) counts these partitions: 822, 552, 5322, 3333, 33222, 222222.
MATHEMATICA
p[n_] := IntegerPartitions[n, All, Fibonacci@Range[3, 60]]; Table[p[n], {n, 0, 12}] (*shows partitions*)
a[n_] := Length@p@n; a /@ Range[0, 80] (*counts partitions, A238999*)
PROG
(PARI) N=66; q='q+O('q^N); Vec( 1/prod(n=1, 11, 1-q^fibonacci(n+2)) ) \\ Joerg Arndt, Mar 11 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 08 2014
STATUS
approved