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A041480 Numerators of continued fraction convergents to sqrt(257). 2
16, 513, 16432, 526337, 16859216, 540021249, 17297539184, 554061275137, 17747258343568, 568466328269313, 18208669762961584, 583245898743040001, 18682077429540241616, 598409723644030771713, 19167793234038524936432, 613967793212876828737537 (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 (32,1).

FORMULA

a(n) = 32*a(n-1)+a(n-2), n>1 ; a(0)=16, a(1)=513. G.f.: (16+x)/(1-32*x-x^2). - Philippe Deléham, Nov 23 2008

a(n) = 8*{[16-sqrt(257)]^n+[16+sqrt(257)]^n}+(1/2)*sqrt(257)*{[16+sqrt(257)]^n -[16-sqrt(257)]^n}, with n>=0. - Paolo P. Lava, Nov 28 2008

MATHEMATICA

Numerator[Convergents[Sqrt[257], 40]] (* or *) LinearRecurrence[{32, 1}, {16, 513}, 40] (* Harvey P. Dale, Aug 13 2012 *)

CROSSREFS

Cf. A041481.

Sequence in context: A013825 A099772 A041483 * A227402 A263907 A222099

Adjacent sequences:  A041477 A041478 A041479 * A041481 A041482 A041483

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Nov 07 2013

STATUS

approved

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Last modified April 29 09:07 EDT 2017. Contains 285604 sequences.