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A042218 Numerators of continued fraction convergents to sqrt(635). 2
25, 126, 6325, 31751, 1593875, 8001126, 401650175, 2016252001, 101214250225, 508087503126, 25505589406525, 128036034535751, 6427307316194075, 32264572615506126, 1619655938091500375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,252,0,-1).

FORMULA

G.f.: (25 +126*x +25*x^2 -x^3)/(x^4 -252*x^2 +1). - Vincenzo Librandi, Nov 19 2013

a(n) = 252*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 19 2013

MATHEMATICA

Numerator[Convergents[Sqrt[635], 30]] (* Harvey P. Dale, Dec 15 2012 *)

CoefficientList[Series[(25 + 126 x + 25 x^2 - x^3)/(x^4 - 252 x^2 + 1), {x, 0, 30}], x](* Vincenzo Librandi, Nov 19 2013 *)

PROG

(Magma) I:=[25, 126, 6325, 31751]; [n le 4 select I[n] else 252*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

CROSSREFS

Cf. A042219.

Sequence in context: A201842 A057902 A042216 * A045166 A232873 A232856

Adjacent sequences: A042215 A042216 A042217 * A042219 A042220 A042221

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)