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%I #14 Jun 13 2015 00:54:08
%S 3,39,390,3630,33033,298389,2688780,24208860,217909263,1961271939,
%T 17651713170,158866215690,1429798332693,12868192168689,
%U 115813751041560,1042323823944120,9380914609207323,84428232063996639,759854090319361950
%N Second elementary symmetric function of the first n terms of (1,3,9,27,81,...).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).
%F a(n) =3*A006100(n).
%F From _Colin Barker_, Aug 15 2014: (Start)
%F a(n) = (3-4*3^n+9^n)/16.
%F a(n) = 13*a(n-1)-39*a(n-2)+27*a(n-3).
%F G.f.: -3*x^2 / ((x-1)*(3*x-1)*(9*x-1)). (End)
%t f[k_] := 3^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
%t a[n_] := SymmetricPolynomial[2, t[n]]
%t Table[a[n], {n, 2, 32}] (* A203243 *)
%t Table[a[n]/3, {n, 2, 32}] (* A006100 *)
%o (PARI) Vec(-3*x^2/((x-1)*(3*x-1)*(9*x-1)) + O(x^100)) \\ _Colin Barker_, Aug 15 2014
%Y Cf. A006100.
%K nonn,easy
%O 2,1
%A _Clark Kimberling_, Dec 31 2011
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