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 A162561 #12 Sep 08 2022 08:45:46 %S A162561 4,23,142,914,6016,40052,268168,1800536,12105664,81444848,548123872, %T A162561 3689452064,24835795456,167190009152,1125512591488,7576945713536, %U A162561 51008180122624,343388995528448,2311709992586752,15562542024241664 %N A162561 a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2. %C A162561 Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766. %H A162561 Harvey P. Dale, <a href="/A162561/b162561.txt">Table of n, a(n) for n = 0..1000</a> %H A162561 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -22). %F A162561 a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23. %F A162561 G.f.: (4-17*x)/(1-10*x+22*x^2). %t A162561 LinearRecurrence[{10,-22},{4,23},30] (* _Harvey P. Dale_, Mar 27 2013 *) %o A162561 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 14 2009 %Y A162561 Cf. A077236, A162559, A162766. %K A162561 nonn %O A162561 0,1 %A A162561 Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009 %E A162561 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 14 2009