A239000 - OEIS

%I #10 Mar 13 2014 23:02:42

%S 1,0,0,1,0,1,1,0,2,1,1,2,1,3,2,2,4,2,4,4,3,7,4,5,8,5,9,8,7,12,9,11,13,

%T 11,17,14,15,20,16,22,22,20,29,24,27,33,28,37,36,35,45,40,46,50,47,60,

%U 55,58,69,62,75,76,73,91,84,91,102,95,114,112,113

%N Number of partitions of n using Fibonacci numbers > 2.

%H Alois P. Heinz, <a href="/A239000/b239000.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1/Product_{i>=4} (1 - x^Fibonacci(i)).

%e a(21) counts these partitions: [21], [13,8], [13,5,3], [8,8,5], [8,5,5,3], [5,5,5,3,3], [3,3,3,3,3,3,3].

%t p[n_] := IntegerPartitions[n, All, Fibonacci@Range[4, 60]]; Table[p[n], {n, 0, 12}] (*shows partitions*)

%t a[n_] := Length@p@n; a /@ Range[0, 80] (*counts partitions, A239000*)

%o (PARI) N=66; q='q+O('q^N); Vec( 1/prod(n=1,11,1-q^fibonacci(n+3)) ) \\ _Joerg Arndt_, Mar 11 2014

%Y Cf. A000045, A003107, A238999.

%K nonn,easy

%O 0,9

%A _Clark Kimberling_, Mar 08 2014