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 A153596 #25 Sep 08 2022 08:45:40
%S A153596 1,10,78,560,3884,26520,179752,1214080,8186256,55152800,371430368,
%T A153596 2500942080,16837952704,113358801280,763153053312,5137636904960,
%U A153596 34587001876736,232842006858240,1567506027294208,10552536122060800,71040228620135424
%N A153596 a(n) = ((5 + sqrt(3))^n - (5 - sqrt(3))^n)/(2*sqrt(3)).
%C A153596 Third binomial transform of A054485. Fifth binomial transform of A162813 preceded by 1.
%C A153596 Lim_{n -> infinity} a(n)/a(n-1) = 5 + sqrt(3) = 6.73205080756887729....
%H A153596 G. C. Greubel, <a href="/A153596/b153596.txt">Table of n, a(n) for n = 1..1000</a>
%H A153596 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-22).
%F A153596 G.f.: x/(1 - 10*x + 22*x^2). - _Klaus Brockhaus_, Dec 31 2008 [corrected Oct 11 2009]
%F A153596 a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0)=0, a(1)=1. - _Philippe Deléham_, Jan 01 2009
%F A153596 E.g.f.: sinh(sqrt(3)*x)*exp(5*x)/sqrt(3). - _Ilya Gutkovskiy_, Aug 23 2016
%t A153596 Table[Simplify[((5+Sqrt[3])^n -(5-Sqrt[3])^n)/(2*Sqrt[3])], {n,1,25}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011, modified by _G. C. Greubel_, Jun 01 2019 *)
%t A153596 LinearRecurrence[{10,-22},{1,10},25] (* _G. C. Greubel_, Aug 22 2016 *)
%o A153596 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((5+r)^n-(5-r)^n)/(2*r): n in [1..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 31 2008
%o A153596 (Sage) [lucas_number1(n,10,22) for n in range(1, 25)] # _Zerinvary Lajos_, Apr 26 2009
%o A153596 (Magma) I:=[1,10]; [n le 2 select I[n] else 10*Self(n-1)-22*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Aug 23 2016
%o A153596 (PARI) my(x='x+O('x^25)); Vec(x/(1-10*x+22*x^2)) \\ _G. C. Greubel_, Jun 01 2019
%Y A153596 Cf. A002194 (decimal expansion of sqrt(3)), A054485, A162813.
%K A153596 nonn
%O A153596 1,2
%A A153596 Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
%E A153596 Extended beyond a(7) by _Klaus Brockhaus_, Dec 31 2008
%E A153596 Edited by _Klaus Brockhaus_, Oct 11 2009