cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A238999 Number of partitions of n using Fibonacci numbers > 1.

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%I A238999 #11 Mar 13 2014 23:03:31
%S A238999 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,
%T A238999 47,53,56,64,69,75,86,89,101,109,117,131,139,151,168,175,195,208,223,
%U A238999 245,259,280,304,320,350,370,397,430,452,488,521,550,596,626
%N A238999 Number of partitions of n using Fibonacci numbers > 1.
%H A238999 Alois P. Heinz, <a href="/A238999/b238999.txt">Table of n, a(n) for n = 0..1000</a>
%F A238999 G.f.: 1/Product_{i>=3} (1 - x^Fibonacci(i)).
%e A238999 a(12) counts these partitions:  822, 552, 5322, 3333, 33222, 222222.
%t A238999 p[n_] := IntegerPartitions[n, All, Fibonacci@Range[3, 60]]; Table[p[n], {n, 0, 12}] (*shows partitions*)
%t A238999 a[n_] := Length@p@n; a /@ Range[0, 80] (*counts partitions, A238999*)
%o A238999 (PARI) N=66; q='q+O('q^N); Vec( 1/prod(n=1,11,1-q^fibonacci(n+2)) ) \\ _Joerg Arndt_, Mar 11 2014
%Y A238999 Cf. A003107, A000045, A239000.
%K A238999 nonn,easy
%O A238999 0,6
%A A238999 _Clark Kimberling_, Mar 08 2014