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 A162816 #19 Apr 18 2024 06:11:51 %S A162816 5,33,231,1683,12573,95337,729135,5603499,43180533,333250929, %T A162816 2574053559,19891362051,153752577165,1188615978297,9189556693119, %U A162816 71050353033627,549348865530597,4247524736257473,32841784272579975,253933094974463091 %N A162816 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33. %C A162816 Binomial transform of A143647. %H A162816 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-33). %F A162816 a(n) = ((5+sqrt(3))*(6+sqrt(3))^n+(5-sqrt(3))*(6-sqrt(3))^n)/2. %F A162816 G.f.: (5-27*x)/(1-12*x+33*x^2). %t A162816 LinearRecurrence[{12,-33},{5,33},40] (* or *) Simplify[With[ {c=Sqrt[3]},Table[(11(5+c)(6+c)^n+(53+7c)(6-c)^n)/(22(6+c)),{n,30}]]] (* _Harvey P. Dale_, Jun 30 2011 *) %o A162816 (Magma) [ n le 2 select 28*n-23 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ]; %o A162816 (PARI) Vec((5-27*x)/(1-12*x+33*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 30 2011 %Y A162816 Cf. A143647. %K A162816 nonn,easy %O A162816 0,1 %A A162816 _Klaus Brockhaus_, Jul 14 2009