%I #19 Jan 01 2024 11:43:21
%S 0,9,170,3059,54900,985149,17677790,317215079,5692193640,102142270449,
%T 1832868674450,32889493869659,590178020979420,10590314883759909,
%U 190035489886698950,3410048503076821199,61190837565496082640
%N a(n+2)=18a(n+1)-a(n)+8.
%C Arises in calculating A107075. A053606 follows the same recurrence.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-19,1).
%F a(n+1) = 9*a(n+1)+4+(80*a(n)^2+80*a(n)+25)^0.5.
%F G.f.: f(z)=a(0)+a(1)*z+a(2)*z^2+...=(9*z-z^2)/((1-z)*(1-18*z+z^2))
%F a(n) = ((sqrt(5)+2)/8)*(9+4*sqrt(5))^n+((-sqrt(5)+2)/8)*(9-4*sqrt(5))^n-0.5 [From _Richard Choulet_, Nov 26 2008]
%F a(n) = (Lucas(6*n-3)-4)/8, where Lucas=A000032(n). [_Gary Detlefs_, Dec 07 2010]
%K nonn,easy
%O 1,2
%A _Richard Choulet_, Aug 30 2007, Oct 09 2007
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