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 A162562 #16 Mar 08 2024 11:58:49
%S A162562 5,8,26,68,188,512,1400,3824,10448,28544,77984,213056,582080,1590272,
%T A162562 4344704,11869952,32429312,88598528,242055680,661308416,1806728192,
%U A162562 4936073216,13485602816,36843352064,100657909760,275002523648
%N A162562 a(n) = ((5+sqrt(3))*(1+sqrt(3))^n + (5-sqrt(3))*(1-sqrt(3))^n)/2.
%C A162562 Binomial transform of A162813. Inverse binomial transform of A162563.
%H A162562 Harvey P. Dale, <a href="/A162562/b162562.txt">Table of n, a(n) for n = 0..1000</a>
%H A162562 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2).
%F A162562 a(n) = 2*a(n-1) + 2*a(n-2) for n > 1; a(0) = 5, a(1) = 8.
%F A162562 G.f.: (5-2*x)/(1-2*x-2*x^2).
%t A162562 LinearRecurrence[{2,2},{5,8},30] (* _Harvey P. Dale_, Aug 17 2013 *)
%o A162562 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((5+r)*(1+r)^n+(5-r)*(1-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 14 2009
%Y A162562 Cf. A162813, A162563.
%K A162562 nonn
%O A162562 0,1
%A A162562 Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
%E A162562 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 14 2009