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 A154250 #25 Sep 08 2022 08:45:40 %S A154250 1,18,250,3168,38524,459000,5411224,63436032,741418000,8651257632, %T A154250 100857705376,1175245632000,13690951178176,159468944439168, %U A154250 1857310612720000,21630889140461568,251915019187028224 %N A154250 a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)). %C A154250 lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(7) = 11.6457513110.... %H A154250 Harvey P. Dale, <a href="/A154250/b154250.txt">Table of n, a(n) for n = 1..938</a> %H A154250 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-74). %F A154250 From _Philippe Deléham_, Jan 06 2009: (Start) %F A154250 a(n) = 18*a(n-1) - 74*a(n-2) for n>1, with a(0)=0, a(1)=1. %F A154250 G.f.: x/(1 - 18*x + 74*x^2). (End) %t A154250 Join[{a=1,b=18},Table[c=18*b-74*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*) %t A154250 LinearRecurrence[{18,-74},{1,18},20] (* _Harvey P. Dale_, Feb 16 2014 *) %o A154250 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jan 07 2009 %Y A154250 Cf. A010465 (decimal expansion of square root of 7). %K A154250 nonn %O A154250 1,2 %A A154250 Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009 %E A154250 Extended beyond a(7) by _Klaus Brockhaus_, Jan 07 2009 %E A154250 Edited by _Klaus Brockhaus_, Oct 06 2009