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 A119032 a(n+2)=18a(n+1)-a(n)+8. 3
 0, 9, 170, 3059, 54900, 985149, 17677790, 317215079, 5692193640, 102142270449, 1832868674450, 32889493869659, 590178020979420, 10590314883759909, 190035489886698950, 3410048503076821199, 61190837565496082640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Arises in calculating A107075. A053606 follows the same recurrence. LINKS Index entries for linear recurrences with constant coefficients, signature (19,-19,1). FORMULA a(n+1) = 9*a(n+1)+4+(80*a(n)^2+80*a(n)+25)^0.5. G.f.: f(z)=a(0)+a(1)*z+a(2)*z^2+...=(9*z-z^2)/((1-z)*(1-18*z+z^2)) a(n) = -(1/2)-(1/8)*sqrt(5)*{[9-4*sqrt(5)]^n-[9+4*sqrt(5))^n}+(1/4)*{[9-4*sqrt(5)]^n+[9+4*sqrt(5)]^n}, with n>=0. [Paolo P. Lava, Nov 25 2008] 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] a(n) = (Lucas(6*n-3)-4)/8, where Lucas=A000032(n). [Gary Detlefs, Dec 07 2010] CROSSREFS Sequence in context: A122725 A012130 A151997 * A215554 A121476 A121477 Adjacent sequences:  A119029 A119030 A119031 * A119033 A119034 A119035 KEYWORD nonn,easy AUTHOR Richard Choulet, Aug 30 2007, Oct 09 2007 STATUS approved

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Last modified April 15 13:37 EDT 2021. Contains 342977 sequences. (Running on oeis4.)