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A042208 Numerators of continued fraction convergents to sqrt(630). 2
25, 251, 12575, 126001, 6312625, 63252251, 3168925175, 31752504001, 1590794125225, 15939693756251, 798575481937775, 8001694513134001, 400883301138637825, 4016834705899512251, 201242618596114250375 (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 (0,502,0,-1).

FORMULA

G.f.: (25 +251*x +25*x^2 -x^3)/(x^4 -502*x^2 +1). - Vincenzo Librandi, Nov 19 2013

a(n) = 502*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 19 2013

MATHEMATICA

Numerator[Convergents[Sqrt[630], 30]] (* or *) CoefficientList[Series[(25 + 251 x + 25 x^2 - x^3)/(x^4 - 502 x^2 + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

LinearRecurrence[{0, 502, 0, -1}, {25, 251, 12575, 126001}, 20] (* Harvey P. Dale, Apr 01 2018 *)

PROG

(MAGMA) I:=[25, 251, 12575, 126001]; [n le 4 select I[n] else 502*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

CROSSREFS

Cf. A042209.

Sequence in context: A023073 A022685 A308492 * A143009 A090022 A298068

Adjacent sequences:  A042205 A042206 A042207 * A042209 A042210 A042211

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 24 20:32 EDT 2022. Contains 354830 sequences. (Running on oeis4.)