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 A162769 #12 Sep 08 2022 08:45:46
%S A162769 1,9,61,389,2441,15249,95141,593389,3700561,23077209,143911501,
%T A162769 897442709,5596515161,34900251489,217640345141,1357219994749,
%U A162769 8463716161441,52780309349289,329141597018461,2052549373305509
%N A162769 a(n) = ((1+sqrt(5))*(4+sqrt(5))^n + (1-sqrt(5))*(4-sqrt(5))^n)/2.
%C A162769 Binomial transform of A082762. Fourth binomial transform of A162962. Inverse binomial transform of A093145 without initial 0.
%H A162769 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-11).
%F A162769 a(n) = 8*a(n-1) - 11*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%F A162769 G.f.: (1+x)/(1-8*x+11*x^2).
%F A162769 a(n) = A091870(n)+A091870(n+1). - _R. J. Mathar_, Feb 04 2021
%t A162769 f[n_] := Block[{s = Sqrt@ 5}, Simplify[((1 + s)(4 + s)^n + (1 - s)(4 - s)^n)/2]]; Array[f, 21, 0] (* Or *)
%t A162769 a[n_] := 8 a[n - 1] - 11 a[n - 2]; a[0] = 1; a[1] = 9; Array[a, 22, 0] (* Or *)
%t A162769 CoefficientList[Series[(1 + x)/(1 - 8 x + 11 x^2), {x, 0, 21}], x] (* _Robert G. Wilson v_ *)
%o A162769 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((1+r)*(4+r)^n+(1-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 19 2009
%Y A162769 Cf. A082762, A162962, A093145.
%K A162769 nonn,easy
%O A162769 0,2
%A A162769 Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009
%E A162769 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 19 2009