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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 (list; graph; refs; listen; history; text; internal format)
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

Colin Barker, Table of n, a(n) for n = 1..1000

Michael Maltenfort, Characterizing Additive Systems, The American Mathematical Monthly 124.2 (2017): 132-148. See Fig. 2.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

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

Adjacent sequences:  A282029 A282030 A282031 * A282033 A282034 A282035

KEYWORD

nonn,tabf,easy

AUTHOR

N. J. A. Sloane, Feb 20 2017

STATUS

approved

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Last modified September 23 10:42 EDT 2021. Contains 347612 sequences. (Running on oeis4.)