cp's OEIS Frontend

A282034 Three-set non-British additive number system read by rows.

%I A282034 #16 Apr 16 2020 18:54:40
%S A282034 1,2,3,4,50,51,52,53,54,5,10,15,20,25,100,125,200,225,300,325,400,425,
%T A282034 500,525,600,625,700,725,800,825,900,925,1000,1025,1100,1125,1200,
%U A282034 1225,1300,1325,1400,1425,1500,1525,1600,1625,1700,1725,1800,1825,1900,1925
%N A282034 Three-set non-British additive number system read by rows.
%C A282034 Any positive integer can be written uniquely as a sum of at most 3 numbers, one from each row of the following array:
%C A282034 1, 2, 3, 4, 50, 51, 52, 53, 54;
%C A282034 5, 10, 15, 20;
%C A282034 25, 100, 125, 200, 225, 300, 325, 400, 425, 500, 525, 600, 625, 700, 725, 800, 825, 900, 925, 1000, ...
%C A282034 (the last row being infinite).
%H A282034 Colin Barker, <a href="/A282034/b282034.txt">Table of n, a(n) for n = 1..1000</a>
%H A282034 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. 5.
%H A282034 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A282034 From _Colin Barker_, Apr 16 2020: (Start)
%F A282034 G.f.: x*(1 + x + 45*x^4 - 45*x^6 - 50*x^9 + 4*x^10 + 54*x^11 + 70*x^14 + 20*x^15) / ((1 - x)^2*(1 + x)).
%F A282034 a(n) = a(n-1) + a(n-2) - a(n-3) for n>16.
%F A282034 (End)
%o A282034 (PARI) Vec(x*(1 + x + 45*x^4 - 45*x^6 - 50*x^9 + 4*x^10 + 54*x^11 + 70*x^14 + 20*x^15) / ((1 - x)^2*(1 + x)) + O(x^50)) \\ _Colin Barker_, Apr 16 2020
%Y A282034 A032174 and A282032 are two other examples of additive number systems.
%K A282034 nonn,tabf,easy
%O A282034 1,2
%A A282034 _N. J. A. Sloane_, Feb 20 2017