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 A163348 #9 Sep 08 2022 08:45:46
%S A163348 1,7,35,161,721,3199,14147,62489,275905,1218007,5376707,23734193,
%T A163348 104768209,462469903,2041441955,9011362409,39778080769,175588947751,
%U A163348 775087121123,3421400092481,15102790707025,66666943594783
%N A163348 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%C A163348 Binomial transform of A111566. Third binomial transform of A143095. Inverse binomial transform of A081180 without initial 0.
%H A163348 G. C. Greubel, <a href="/A163348/b163348.txt">Table of n, a(n) for n = 0..1000</a>
%H A163348 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-7).
%F A163348 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
%F A163348 a(n) = ((1+2*sqrt(2))*(3+sqrt(2))^n + (1-2*sqrt(2))*(3-sqrt(2))^n)/2.
%F A163348 G.f.: (1+x)/(1-6*x+7*x^2).
%F A163348 E.g.f.: exp(3*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 19 2016
%F A163348 a(n) = A081179(n)+A081179(n+1). - _R. J. Mathar_, Feb 04 2021
%t A163348 LinearRecurrence[{6, -7}, {1, 7}, 50] (* _G. C. Greubel_, Dec 19 2016 *)
%o A163348 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(3+r)^n+(1-2*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 26 2009
%o A163348 (PARI) Vec((1+x)/(1-6*x+7*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 19 2016
%Y A163348 Cf. A111566, A143095 (1,4,2,8,4,16,...), A081180.
%K A163348 nonn,easy
%O A163348 0,2
%A A163348 Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
%E A163348 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 26 2009