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.

A163072 a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.

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%I A163072 #6 Sep 08 2022 08:45:46
%S A163072 4,25,170,1200,8600,62000,448000,3240000,23440000,169600000,
%T A163072 1227200000,8880000000,64256000000,464960000000,3364480000000,
%U A163072 24345600000000,176166400000000,1274752000000000,9224192000000000,66746880000000000
%N A163072 a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.
%C A163072 Binomial transform of A108404 without initial 1. Fifth binomial transform of A163141.
%H A163072 G. C. Greubel, <a href="/A163072/b163072.txt">Table of n, a(n) for n = 0..1000</a>
%H A163072 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-20).
%F A163072 a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 4, a(1) = 25.
%F A163072 G.f.: (4-15*x)/(1-10*x+20*x^2).
%t A163072 LinearRecurrence[{10, -20}, {4, 25}, 30] (* _G. C. Greubel_, Jan 08 2018 *)
%o A163072 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); 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 21 2009
%o A163072 (PARI) x='x+O('x^30); Vec((4-15*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Jan 08 2018
%Y A163072 Cf. A108404, A163141.
%K A163072 nonn
%O A163072 0,1
%A A163072 Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
%E A163072 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 21 2009