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A041220 Numerators of continued fraction convergents to sqrt(122). 2
11, 243, 5357, 118097, 2603491, 57394899, 1265291269, 27893802817, 614928953243, 13556330774163, 298854205984829, 6588348862440401, 145242529179673651, 3201923990815260723, 70587570327115409557, 1556128471187354270977, 34305413936448909371051 (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 (22,1).

FORMULA

a(n) = 22*a(n-1) + a(n-2) for n>1, a(0)=11, a(1)=243. G.f.: (11+x) / (1-22*x-x^2). [Philippe Deléham, Nov 21 2008]

a(n) = (11/2)*((11+sqrt(122))^n+(11-sqrt(122))^n)+(1/2)*sqrt(122)*((11+sqrt(122))^n-(11-sqrt(122))^n). [Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator/@Convergents[Sqrt[122], 20] (* Harvey P. Dale, Jun 04 2011 *)

CoefficientList[Series[(11 + x)/(1 - 22 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 31 2013 *)

CROSSREFS

Cf. A041221.

Sequence in context: A196258 A121826 A041223 * A219089 A243683 A167868

Adjacent sequences:  A041217 A041218 A041219 * A041221 A041222 A041223

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 July 20 16:53 EDT 2017. Contains 289628 sequences.