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 A163616 #12 Sep 08 2022 08:45:46
%S A163616 1,11,87,617,4169,27499,179103,1158553,7466161,48014891,308427207,
%T A163616 1979929577,12705470009,81516319819,522937387983,3354498523993,
%U A163616 21517425316321,138020787111371,885307088838327,5678592784821737
%N A163616 a(n) = ((1 + 3*sqrt(2))*(5 + sqrt(2))^n + (1 - 3*sqrt(2))*(5 - sqrt(2))^n)/2.
%C A163616 Binomial transform of A163615. Fifth binomial transform of A163864. Inverse binomial transform of A081183 without initial 0.
%H A163616 G. C. Greubel, <a href="/A163616/b163616.txt">Table of n, a(n) for n = 0..1000</a>
%H A163616 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A163616 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
%F A163616 G.f.: (1+x)/(1-10*x+23*x^2).
%F A163616 E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Jul 30 2017
%F A163616 a(n) = A081182(n)+A081182(n+1). - _R. J. Mathar_, Jul 01 2022
%t A163616 CoefficientList[Series[(1 + x)/(1 - 10 x + 23 x^2), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jun 14 2014 *)
%t A163616 LinearRecurrence[{10, -23}, {1, 11}, 50] (* _G. C. Greubel_, Jul 30 2017 *)
%o A163616 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(5+r)^n+(1-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 06 2009
%o A163616 (PARI) x='x+O('x^50); Vec((1+x)/(1-10*x+23*x^2)) \\ _G. C. Greubel_, Jul 30 2017
%Y A163616 Cf. A163615, A163864, A081183.
%K A163616 nonn,easy
%O A163616 0,2
%A A163616 Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%E A163616 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 06 2009