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
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Feb 20 2017
STATUS
approved