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 A085480 #27 Jan 10 2021 12:26:05
%S A085480 0,3,15,54,207,783,2970,11259,42687,161838,613575,2326239,8819442,
%T A085480 33437043,126769455,480619494,1822166847,6908359023,26191577610,
%U A085480 99299809899,376474162527,1427321917278,5411388239415,20516130470079
%N A085480 Expansion of 3*x*(1+2*x)/(1-3*x-3*x^2).
%C A085480 A Jacobsthal variation.
%C A085480 p - q = sqrt(21); p*q = -3; p + q = 3.
%D A085480 Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
%H A085480 Harvey P. Dale, <a href="/A085480/b085480.txt">Table of n, a(n) for n = 1..1000</a>
%H A085480 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A085480 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,3).
%F A085480 a(n) = p^n + q^n, where p = (3 + sqrt(21))/2, q = (3 - sqrt 21)/2.
%F A085480 a(n) = 3*a(n-1) + 3*a(n-2), a(1)=3, a(2)=15. - _Philippe Deléham_, Nov 19 2008
%F A085480 G.f.: G(0)/x - 2/x, where G(k) = 1 + 1/(1 - x*(7*k-3)/(x*(7*k+4) - 2/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 03 2013
%e A085480 a(4) = q^4 + q^4 = 207; p^5 + q^5 = 783, where p = (3 + sqrt(21))/2, q = (3 - sqrt(21))/2.
%t A085480 CoefficientList[Series[3x (1+2x)/(1-3x-3x^2),{x,0,30}],x] (* or *) LinearRecurrence[{3,3},{0,3,15},30] (* _Harvey P. Dale_, Jan 10 2021 *)
%Y A085480 Cf. A030195.
%K A085480 nonn,easy
%O A085480 1,2
%A A085480 _Gary W. Adamson_, Jul 02 2003
%E A085480 Zero prepended by _Harvey P. Dale_, Jan 10 2021