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A119032 a(n+2)=18a(n+1)-a(n)+8. 3

%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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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)