OFFSET
1,2
COMMENTS
The five sets are the following:
1, 2, 3, 4;
5;
10, 20;
25, 50, 75;
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, ...
(the last set being infinite).
In contrast to A282032 this is not an additive number system because 26 for example can be represented in two ways as a sum of numbers from distinct sets (26 = 1+5+20 = 1+25).
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. 3.
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 + 5*x^6 - 5*x^7 + 20*x^8 + 75*x^11) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>12.
(End)
MATHEMATICA
LinearRecurrence[{2, -1}, {1, 2, 3, 4, 5, 10, 20, 25, 50, 75, 100, 200, 300, 400}, 50] (* or *) CoefficientList[Series[x (1+4x^5+5x^6-5x^7+ 20x^8+ 75x^11)/ (1-x)^2, {x, 0, 50}], x] (* Harvey P. Dale, Aug 04 2021 *)
PROG
(PARI) Vec(x*(1 + 4*x^5 + 5*x^6 - 5*x^7 + 20*x^8 + 75*x^11) / (1 - x)^2 + O(x^50)) \\ Colin Barker, Apr 16 2020
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Feb 20 2017
STATUS
approved