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%I #27 Apr 10 2016 10:58:04
%S 3,7,18,49,138,397,1158,3409,10098,30037,89598,267769,801258,2399677,
%T 7190838,21556129,64635618,193841317,581392878,1743916489,5231225178,
%U 15692626957,47075783718,141223156849,423661081938,1270966468597,3812865851358,11438530445209,34315457117898,102946102918237
%N a(n) = (1 + 2^n + 3^n)/2.
%H Colin Barker, <a href="/A267799/b267799.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = (A007689(n)+1)/2.
%F From _Colin Barker_, Apr 07 2016: (Start)
%F a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n>3.
%F G.f.: x*(3-11*x+9*x^2) / ((1-x)*(1-2*x)*(1-3*x)).
%F (End)
%F a(n) = A001550(n)/2, for n >= 1. - _Altug Alkan_, Apr 08 2016
%e a(3) = (1 + 2^3 + 3^3)/2 = 18.
%t Table[(1 + 2^n + 3^n)/2, {n, 30}] (* _Michael De Vlieger_, Apr 07 2016 *)
%o (PARI) Vec(x*(3-11*x+9*x^2)/((1-x)*(1-2*x)*(1-3*x)) + O(x^50)) \\ _Colin Barker_, Apr 07 2016
%o (PARI) a(n) = (1 + 2^n + 3^n)/2 \\ _Charles R Greathouse IV_, Apr 07 2016
%Y Cf. A000079, A000244, A001550, A007689.
%K nonn,easy
%O 1,1
%A _Emre APARI_, Apr 07 2016
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