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A041144 Numerators of continued fraction convergents to sqrt(82). 2
9, 163, 2943, 53137, 959409, 17322499, 312764391, 5647081537, 101960232057, 1840931258563, 33238722886191, 600137943210001, 10835721700666209, 195643128555201763, 3532412035694297943, 63779059771052564737, 1151555487914640463209, 20791777842234580902499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (18,1).

FORMULA

a(n)=18*a(n-1)+a(n-2), n>1 ; a(0)=9, a(1)=163 . G.f.: (9+x)/(1-18*x-x^2). [From Philippe Deléham, Nov 21 2008]

a(n)=(9/2)*{[9-sqrt(82)]^n+[9+sqrt(82)]^n}+(1/2)*sqrt(82)*{[9+sqrt(82)]^n-[9-sqrt(82)]^n}, with n>=0 [From Paolo P. Lava, Nov 28 2008]

MATHEMATICA

CoefficientList[Series[(9 + x)/(1 - 18 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

CROSSREFS

Cf. A010533, A041145.

Sequence in context: A157574 A077280 A041147 * A212334 A086759 A053130

Adjacent sequences:  A041141 A041142 A041143 * A041145 A041146 A041147

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 05 2013

STATUS

approved

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Last modified June 27 19:44 EDT 2017. Contains 288790 sequences.