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%I M4066 #43 Mar 13 2023 06:53:22
%S 1,6,8,10,12,15,17,19,24,26,28,33,35,37,42,44,46,51,53,55,60,62,64,69,
%T 71,73,78,80,82,87,89,91,96,98,100,105,107,109,114,116,118,123,125,
%U 127,132,134,136,141,143,145,150,152,154,159,161,163,168,170,172,177,179
%N a(n) is smallest number != a(j) + a(k), j < k and a(1) = 1, a(2) = 6.
%C Numbers congruent to {1, 6, 8} mod 9 plus the number 12.
%D R. K. Guy, "s-Additive sequences", preprint, 1994.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003663/b003663.txt">Table of n, a(n) for n = 1..2000</a>
%H S. R. Finch, <a href="http://www.jstor.org/stable/2325001">Are 0-additive sequences always regular?</a>, Amer. Math. Monthly, 99 (1992), 671-673.
%H R. K. Guy, <a href="/A007300/a007300.pdf">s-Additive sequences</a>, Preprint, 1994. (Annotated scanned copy)
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _Chai Wah Wu_, Feb 21 2018: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n > 9.
%F 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)
%t 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 *)
%t LinearRecurrence[{1,0,1,-1},{1,6,8,10,12,15,17,19,24},70] (* _Harvey P. Dale_, Jul 25 2018 *)
%o (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
%Y Cf. A199162, A060469, A060470, A060471, A060472.
%Y Cf. A003662, A005408, A026471, A026474, A033627, A051039, A051040, A244151.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E Name clarified by _David A. Corneth_, Mar 13 2023
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