cp's OEIS Frontend

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.

A162773 a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.

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%I A162773 #13 Sep 08 2022 08:45:46
%S A162773 2,15,110,800,5800,42000,304000,2200000,15920000,115200000,833600000,
%T A162773 6032000000,43648000000,315840000000,2285440000000,16537600000000,
%U A162773 119667200000000,865920000000000,6265856000000000,45340160000000000
%N A162773 a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.
%C A162773 Binomial transform of A162772. Fifth binomial transform of A162963.
%H A162773 Harvey P. Dale, <a href="/A162773/b162773.txt">Table of n, a(n) for n = 0..1000</a>
%H A162773 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -20).
%F A162773 a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 2, a(1) = 15.
%F A162773 G.f.: (2-5*x)/(1-10*x+20*x^2).
%t A162773 LinearRecurrence[{10,-20},{2,15},30] (* _Harvey P. Dale_, Dec 24 2012 *)
%o A162773 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(5+r)^n+(2-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 19 2009
%Y A162773 Cf. A162772, A162963.
%K A162773 nonn
%O A162773 0,1
%A A162773 Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009
%E A162773 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 19 2009
%E A162773 Formulae corrected and clarified by _Harvey P. Dale_, Dec 24 2012