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 A162270 #23 Sep 08 2022 08:45:46
%S A162270 5,17,67,283,1229,5393,23755,104779,462389,2040881,9008563,39765211,
%T A162270 175531325,774831473,3420269563,15097797067,66644895461,294184793297,
%U A162270 1298594491555,5732273396251,25303478936621,111694959845969
%N A162270 a(n) = ((5+sqrt(2))*(3+sqrt(2))^n + (5-sqrt(2))*(3-sqrt(2))^n)/2.
%C A162270 Third binomial transform of A162396.
%H A162270 Harvey P. Dale, <a href="/A162270/b162270.txt">Table of n, a(n) for n = 0..1000</a>
%H A162270 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -7).
%F A162270 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 5, a(1) = 17.
%F A162270 G.f.: (5-13*x)/(1-6*x+7*x^2).
%F A162270 a(n) = 5*A081179(n+1)-13*A081179(n). - _R. J. Mathar_, Feb 04 2021
%p A162270 seq(coeff(series((5-13*x)/(1-6*x+7*x^2),x,n+1), x, n), n = 0..25); # _Muniru A Asiru_, Sep 28 2018
%t A162270 LinearRecurrence[{6,-7},{5,17},30] (* _Harvey P. Dale_, Jun 04 2016 *)
%o A162270 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(3+r)^n+(5-r)*(3-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 02 2009
%o A162270 (Magma) I:=[5,17]; [n le 2 select I[n] else 6*Self(n-1) - 7*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Sep 28 2018
%o A162270 (PARI) x='x+O('x^30); Vec((5-13*x)/(1-6*x+7*x^2)) \\ _G. C. Greubel_, Sep 28 2018
%o A162270 (GAP) a:=[5,17];; for n in [3..25] do a[n]:=6*a[n-1]-7*a[n-2]; od; a; # _Muniru A Asiru_, Sep 28 2018
%Y A162270 Cf. A162396.
%K A162270 nonn,easy
%O A162270 0,1
%A A162270 Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
%E A162270 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 02 2009