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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).
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%I #26 Nov 14 2022 20:01:48

%S 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 60,65,71,76,83,89,96,103,111,119,128,136,146,156,167,178,189,201,214,

%U 227,241,255,270,286,302,319,337,355,375,394,415,436,458,481,505,529,555

%N 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 Alois P. Heinz, <a href="/A089197/b089197.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/((1-x^1)*(1-x^2)*(1-x^5)*(1-x^13)*(1-x^34)*(1-x^89)*...).

%t <<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 Cf. A000045, A003107.

%K easy,nonn

%O 0,3

%A _Wouter Meeussen_, Dec 08 2003

%E Incorrect comment deleted by _Peter Munn_, Nov 14 2022