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A042750 Numerators of continued fraction convergents to sqrt(906). 2
30, 301, 18090, 181201, 10890150, 109082701, 6555852210, 65667604801, 3946612140270, 39531789007501, 2375853952590330, 23798071314910801, 1430260132847238390, 14326399399787294701, 861014224120084920450 (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 (0,602,0,-1).

FORMULA

G.f.: (30 +301*x +30*x^2 -x^3)/(1 -602*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013

a(n) = 602*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

MATHEMATICA

Numerator[Convergents[Sqrt[906], 30]] (* or *) CoefficientList[Series[(30 + 301 x + 30 x^2 - x^3)/(1 - 602 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)

LinearRecurrence[{0, 602, 0, -1}, {30, 301, 18090, 181201}, 20] (* Harvey P. Dale, Jun 11 2017 *)

PROG

(MAGMA) I:=[30, 301, 18090, 181201]; [n le 4 select I[n] else 602*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

CROSSREFS

Cf. A042751.

Sequence in context: A061605 A125393 A126551 * A074994 A134287 A141216

Adjacent sequences:  A042747 A042748 A042749 * A042751 A042752 A042753

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)