This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A203243 #18 Feb 18 2025 03:54:52
%S A203243 3,39,390,3630,33033,298389,2688780,24208860,217909263,1961271939,
%T A203243 17651713170,158866215690,1429798332693,12868192168689,
%U A203243 115813751041560,1042323823944120,9380914609207323,84428232063996639,759854090319361950
%N A203243 Second elementary symmetric function of the first n terms of (1,3,9,27,81,...).
%H A203243 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).
%F A203243 a(n) = 3*A006100(n).
%F A203243 From _Colin Barker_, Aug 15 2014: (Start)
%F A203243 a(n) = (3-4*3^n+9^n)/16.
%F A203243 a(n) = 13*a(n-1)-39*a(n-2)+27*a(n-3).
%F A203243 G.f.: -3*x^2 / ((x-1)*(3*x-1)*(9*x-1)). (End)
%t A203243 f[k_] := 3^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
%t A203243 a[n_] := SymmetricPolynomial[2, t[n]]
%t A203243 Table[a[n], {n, 2, 32}] (* A203243 *)
%t A203243 Table[a[n]/3, {n, 2, 32}] (* A006100 *)
%o A203243 (PARI) Vec(-3*x^2/((x-1)*(3*x-1)*(9*x-1)) + O(x^100)) \\ _Colin Barker_, Aug 15 2014
%Y A203243 Cf. A006100.
%K A203243 nonn,easy
%O A203243 2,1
%A A203243 _Clark Kimberling_, Dec 31 2011