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%I #16 Apr 16 2020 18:54:26
%S 1,2,3,4,5,10,15,20,25,50,100,200,300,400,500,600,700,800,900,1000,
%T 1100,1200,1300,1400,1500,1600,1700,1800,1900,2000,2100,2200,2300,
%U 2400,2500,2600,2700,2800,2900,3000,3100,3200,3300,3400,3500,3600,3700,3800
%N Additive number system based on U.S. coins.
%C Any positive integer can be written uniquely as a sum of at most 5 numbers, one from each row of the following array:
%C 1,2,3,4;
%C 5,10,15,20;
%C 25;
%C 50;
%C 100, 200, 300, 400, 500, ...
%C (the last row being infinite).
%H Colin Barker, <a href="/A282032/b282032.txt">Table of n, a(n) for n = 1..1000</a>
%H Michael Maltenfort, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.124.2.132">Characterizing Additive Systems</a>, The American Mathematical Monthly 124.2 (2017): 132-148. See Fig. 2.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F From _Colin Barker_, Apr 16 2020: (Start)
%F G.f.: x*(1 + 4*x^5 + 20*x^9 + 25*x^10 + 50*x^11) / (1 - x)^2.
%F a(n) = 2*a(n-1) - a(n-2) for n>11.
%F (End)
%o (PARI) Vec(x*(1 + 4*x^5 + 20*x^9 + 25*x^10 + 50*x^11) / (1 - x)^2 + O(x^50)) \\ _Colin Barker_, Apr 16 2020
%Y A032174 and A282034 are two other examples of additive number systems.
%Y A282033 gives a very similar family of sets which is not an additive system.
%K nonn,tabf,easy
%O 1,2
%A _N. J. A. Sloane_, Feb 20 2017
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