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%I #28 Apr 16 2023 08:36:29
%S 2,3,4,8,9,14,15,20,21,26,27,32,33,38,39,44,45,50,51,56,57,62,63,68,
%T 69,74,75,80,81,86,87,92,93,98,99,104,105,110,111,116,117,122,123,128,
%U 129,134,135,140,141,146,147,152,153,158,159,164,165,170,171,176,177,182,183,188,189,194,195,200,201,206,207,212,213
%N 0-additive sequence: start with a(1) = 2; thereafter, a(n) = smallest number not already in sequence which is not the sum of any previous two terms.
%C As A033627, but first term is 2.
%C 4 and the numbers in A047243. - _Joerg Arndt_, Jun 22 2014
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(2n) = 6(n-1)+2 & a(2n+1) = 6(n-1)+3 for n>1. - _Robert G. Wilson v_, Jun 23 2014
%F From _Colin Barker_, Jun 26 2014: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 6.
%F G.f.: x*(x^5 + 3*x^3 - x^2 + x + 2)/((x - 1)^2*(x + 1)). (End)
%F E.g.f.: (x^3 + 3*x^2 + 30*x + 24)/6 + (3*x - 4)*cosh(x) + 3*(x - 2)*sinh(x). - _Stefano Spezia_, Apr 15 2023
%t f[s_List] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {2}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[f, {2}, 70] (* _Robert G. Wilson v_, Jun 23 2014 *)
%o (PARI) Vec(x*(x^5+3*x^3-x^2+x+2)/((x-1)^2*(x+1)) + O(x^100)) \\ _Colin Barker_, Jun 26 2014
%Y Cf. A033627, A047243.
%K nonn,easy
%O 1,1
%A _Leonardo Sznajder_, Jun 21 2014
%E Added terms >= 20, _Joerg Arndt_, Jun 22 2014
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