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%I #18 Jun 13 2015 00:51:49
%S 1,6,21,72,225,702,2133,6480,19521,58806,176661,530712,1592865,
%T 4780782,14344533,43040160,129127041,387400806,1162222101,3486725352,
%U 10460235105,31380882462,94142824533,282429005040,847287546561
%N Sum 3^max(k,n-k),k=0..n.
%C Third column of A107661.
%H Vincenzo Librandi, <a href="/A107660/b107660.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-9).
%F G.f.: (1+3*x)/((1-3*x)*(1-3*x^2)).
%F a(2n) = 3^(2n+1) - 2*3^n; a(2n+1) = 9^(n+1) - 3^(n+1).
%F a(n) = A167993(n+2) + 3*A167993(n+1). - _R. J. Mathar_, Aug 16 2013
%t CoefficientList[Series[(1 + 3 x) / ((1 - 3 x) (1 - 3 x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%Y Cf. A107659, A107661.
%K nonn,easy
%O 0,2
%A _Mitch Harris_
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