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 A162563 #16 Sep 08 2022 08:45:46
%S A162563 5,13,47,175,653,2437,9095,33943,126677,472765,1764383,6584767,
%T A162563 24574685,91713973,342281207,1277410855,4767362213,17792037997,
%U A162563 66400789775,247811121103,924843694637,3451563657445,12881410935143,48074080083127
%N A162563 a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2.
%C A162563 Binomial transform of A162562. Second binomial transform of A162813. Inverse binomial transform of A162814.
%H A162563 Harvey P. Dale, <a href="/A162563/b162563.txt">Table of n, a(n) for n = 0..1000</a>
%H A162563 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1).
%F A162563 a(n) = 4*a(n-1) - a(n-2) for n > 1; a(0) = 5, a(1) = 13.
%F A162563 G.f.: (5-7*x)/(1-4*x+x^2).
%F A162563 a(n) = 4*a(n-1) - a(n-2), with a(0)=5 and a(1)=13. - _Paolo P. Lava_, Jul 15 2009
%t A162563 LinearRecurrence[{4,-1},{5,13},30] (* _Harvey P. Dale_, Aug 25 2014 *)
%o A162563 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((5+r)*(2+r)^n+(5-r)*(2-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 14 2009
%Y A162563 Cf. A162562, A162813, A162814.
%K A162563 nonn
%O A162563 0,1
%A A162563 Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
%E A162563 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 18 2009