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A042190 Numerators of continued fraction convergents to sqrt(620). 2
24, 25, 224, 249, 12176, 12425, 111576, 124001, 6063624, 6187625, 55564624, 61752249, 3019672576, 3081424825, 27671071176, 30752496001, 1503790879224, 1534543375225, 13780137881024, 15314681256249 (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, 0, 0, 498, 0, 0, 0, -1).

FORMULA

G.f.: (24 +25*x +224*x^2 +249*x^3 +224*x^4 -25*x^5 +24*x^6 -x^7)/(1 -498*x^4 +x^8). - Vincenzo Librandi, Nov 18 2013

a(n) = 498*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 18 2013

MATHEMATICA

Numerator[Convergents[Sqrt[620], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 224 x^2 + 249 x^3 + 224 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 498 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

LinearRecurrence[{0, 0, 0, 498, 0, 0, 0, -1}, {24, 25, 224, 249, 12176, 12425, 111576, 124001}, 20] (* Harvey P. Dale, Dec 15 2014 *)

PROG

(MAGMA) I:=[24, 25, 224, 249, 12176, 12425, 111576, 124001]; [n le 8 select I[n] else 498*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

CROSSREFS

Cf. A042191.

Sequence in context: A042184 A042186 A042188 * A042192 A042194 A042196

Adjacent sequences:  A042187 A042188 A042189 * A042191 A042192 A042193

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 23 01:30 EST 2020. Contains 331166 sequences. (Running on oeis4.)