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A041112 Numerators of continued fraction convergents to sqrt(65). 2
8, 129, 2072, 33281, 534568, 8586369, 137916472, 2215249921, 35581915208, 571525893249, 9179996207192, 147451465208321, 2368403439540328, 38041906497853569, 611038907405197432, 9814664424981012481, 157645669707101397128, 2532145379738603366529 (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 (16,1).

FORMULA

a(n) = 16*a(n-1)+a(n-2), with n>1, a(0)=8, a(1)=129 . G.f.: (8+x)/(1-16*x-x^2). [Philippe Deléham, Nov 21 2008]

a(n) = (1/2)*sqrt(65)*((8+sqrt(65))^n-(8-sqrt(65))^n)+4*((8-sqrt(65))^n+(8+sqrt(65))^n). [Paolo P. Lava, Nov 28 2008]

MATHEMATICA

CoefficientList[Series[(8 + x)/(1 - 16 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

Numerator[Convergents[Sqrt[65], 20]] (* or *) LinearRecurrence[{16, 1}, {8, 129}, 20] (* Harvey P. Dale, Nov 12 2013 *)

CROSSREFS

Cf. A010517, A041113.

Sequence in context: A265097 A027951 A041115 * A073701 A239756 A240630

Adjacent sequences:  A041109 A041110 A041111 * A041113 A041114 A041115

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 28 05:58 EDT 2017. Contains 288813 sequences.