%I #24 Sep 08 2022 08:45:40
%S 1,16,198,2240,24356,259776,2743768,28833280,302193936,3162772736,
%T 33077115488,345793029120,3614215767616,37771456592896,
%U 394718790964608,4124756173045760,43102408892784896,450402684247904256
%N a(n) = ( (8 + sqrt(6))^n - (8 - sqrt(6))^n )/(2*sqrt(6)).
%C lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(6) = 10.4494897427....
%H Harvey P. Dale, <a href="/A154240/b154240.txt">Table of n, a(n) for n = 1..981</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -58).
%F From _Philippe Deléham_, Jan 06 2009: (Start)
%F a(n) = 16*a(n-1) - 58*a(n-2) for n>1, with a(0)=0, a(1)=1.
%F G.f.: x/(1 - 16*x + 58*x^2). (End)
%F E.g.f.: sinh(sqrt(6)*x)*exp(8*x)/sqrt(6). - _Ilya Gutkovskiy_, Sep 07 2016
%t Join[{a=1,b=16},Table[c=16*b-58*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2011*)
%t With[{s=Sqrt[6]},Table[Simplify[((8+s)^n-(8-s)^n)/(2s)],{n,20}]] (* or *) LinearRecurrence[{16,-58},{1,16},20] (* _Harvey P. Dale_, Jul 17 2013 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jan 07 2009
%Y Cf. A010464 (decimal expansion of square root of 6).
%K nonn
%O 1,2
%A Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
%E Extended beyond a(7) by _Klaus Brockhaus_, Jan 07 2009
%E Edited by _Klaus Brockhaus_, Oct 06 2009