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A089197 Nonadjacent Fibonacci currency: number of ways to make change for n units in a currency system with coins of value 1, 2, 5, 13, 34, 89, ..., Fibonacci(2k-1).

%I A089197 #26 Nov 14 2022 20:01:48
%S A089197 1,1,2,2,3,4,5,6,7,8,10,11,13,15,17,20,22,25,28,31,35,38,42,46,50,55,
%T A089197 60,65,71,76,83,89,96,103,111,119,128,136,146,156,167,178,189,201,214,
%U A089197 227,241,255,270,286,302,319,337,355,375,394,415,436,458,481,505,529,555
%N A089197 Nonadjacent Fibonacci currency: number of ways to make change for n units in a currency system with coins of value 1, 2, 5, 13, 34, 89, ..., Fibonacci(2k-1).
%H A089197 Alois P. Heinz, <a href="/A089197/b089197.txt">Table of n, a(n) for n = 0..10000</a>
%F A089197 G.f.: 1/((1-x^1)*(1-x^2)*(1-x^5)*(1-x^13)*(1-x^34)*(1-x^89)*...).
%t A089197 <<DiscreteMath`Rsolve`; a[n_Integer] := SeriesTerm[1/(1-x^1)/(1-x^2)/(1-x^5)/(1-x^13)/(1-x^34)/(1-x^89), {x, 0, n}]
%Y A089197 Cf. A000045, A003107.
%K A089197 easy,nonn
%O A089197 0,3
%A A089197 _Wouter Meeussen_, Dec 08 2003
%E A089197 Incorrect comment deleted by _Peter Munn_, Nov 14 2022