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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

Table of n, a(n) for n=1..17.

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 September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)