OFFSET
1,2
COMMENTS
Numbers congruent to {1, 6, 8} mod 9 plus the number 12.
REFERENCES
R. K. Guy, "s-Additive sequences", preprint, 1994.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..2000
S. R. Finch, Are 0-additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671-673.
R. K. Guy, s-Additive sequences, Preprint, 1994. (Annotated scanned copy)
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From Chai Wah Wu, Feb 21 2018: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 9.
G.f.: x*(2*x^8 + x^5 - 3*x^4 + x^3 + 2*x^2 + 5*x + 1)/(x^4 - x^3 - x + 1). (End)
MATHEMATICA
f[s_List, j_Integer] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {j}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#, 2] &, {1, 6}, 65] (* Robert G. Wilson v, Jul 05 2014 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 6, 8, 10, 12, 15, 17, 19, 24}, 70] (* Harvey P. Dale, Jul 25 2018 *)
PROG
(Magma) I:=[1, 6, 8, 10, 12, 15, 17, 19, 24]; [n le 9 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Feb 22 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name clarified by David A. Corneth, Mar 13 2023
STATUS
approved