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

1, 2, 3, 4, 50, 51, 52, 53, 54, 5, 10, 15, 20, 25, 100, 125, 200, 225, 300, 325, 400, 425, 500, 525, 600, 625, 700, 725, 800, 825, 900, 925, 1000, 1025, 1100, 1125, 1200, 1225, 1300, 1325, 1400, 1425, 1500, 1525, 1600, 1625, 1700, 1725, 1800, 1825, 1900, 1925

Offset

1,2

Comments

Any positive integer can be written uniquely as a sum of at most 3 numbers, one from each row of the following array:

1, 2, 3, 4, 50, 51, 52, 53, 54;

5, 10, 15, 20;

25, 100, 125, 200, 225, 300, 325, 400, 425, 500, 525, 600, 625, 700, 725, 800, 825, 900, 925, 1000, ...

(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. 5.

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

Formula

From Colin Barker, Apr 16 2020: (Start)

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)).

a(n) = a(n-1) + a(n-2) - a(n-3) for n>16.

(End)

Prog

(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

Crossrefs

A032174 and A282032 are two other examples of additive number systems.

Sequence in context: A257482 A023167 A177380 * A096782 A098811 A169902

Adjacent sequences: A282031 A282032 A282033 * A282035 A282036 A282037

Keyword

nonn,tabf,easy

Author

N. J. A. Sloane, Feb 20 2017

Status

approved