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%I #15 Sep 08 2022 08:45:40
%S 1,18,246,3024,35244,398520,4424328,48553344,528862608,5732366112,
%T 61931306592,667638961920,7186859400384,77287630177152,
%U 830602309958784,8922406425440256,95816335481139456,1028746337476170240,11043759907042186752,118545464003618082816
%N a(n) = ((9 + sqrt(3))^n - (9 - sqrt(3))^n)/(2*sqrt(3)).
%C lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(3) = 10.73205080756887729....
%H G. C. Greubel, <a href="/A153600/b153600.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-78).
%F G.f.: x/(1 - 18*x + 78*x^2). - _Klaus Brockhaus_, Dec 31 2008, (corrected Oct 11 2009)
%F a(n) = 18*a(n-1) - 78*a(n-2) for n>1; a(0)=0, a(1)=1. - _Philippe Deléham_, Jan 01 2009
%t Join[{a=1,b=18},Table[c=18*b-78*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*)
%t LinearRecurrence[{18, -78}, {1, 18}, 25] (* _G. C. Greubel_, Aug 22 2016 *)
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 31 2008
%o (Magma) I:=[1,18]; [n le 2 select I[n] else 18*Self(n-1)-78*Self(n-2): n in [1..25]]; // _Vincenzo Librandi_, Aug 23 2016
%Y Cf. A002194 (decimal expansion of sqrt(3)).
%K nonn
%O 1,2
%A Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
%E Extended beyond a(7) by _Klaus Brockhaus_, Dec 31 2008
%E Edited by _Klaus Brockhaus_, Oct 11 2009
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