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A282032
Additive number system based on U.S. coins.
3
1, 2, 3, 4, 5, 10, 15, 20, 25, 50, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 3100, 3200, 3300, 3400, 3500, 3600, 3700, 3800
OFFSET
1,2
COMMENTS
Any positive integer can be written uniquely as a sum of at most 5 numbers, one from each row of the following array:
1,2,3,4;
5,10,15,20;
25;
50;
100, 200, 300, 400, 500, ...
(the last row being infinite).
LINKS
Michael Maltenfort, Characterizing Additive Systems, The American Mathematical Monthly 124.2 (2017): 132-148. See Fig. 2.
FORMULA
From Colin Barker, Apr 16 2020: (Start)
G.f.: x*(1 + 4*x^5 + 20*x^9 + 25*x^10 + 50*x^11) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>11.
(End)
PROG
(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
CROSSREFS
A032174 and A282034 are two other examples of additive number systems.
A282033 gives a very similar family of sets which is not an additive system.
Sequence in context: A032543 A140730 A273732 * A205962 A134220 A179146
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Feb 20 2017
STATUS
approved