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A041646 Numerators of continued fraction convergents to sqrt(342). 2
18, 37, 1350, 2737, 99882, 202501, 7389918, 14982337, 546754050, 1108490437, 40452409782, 82013310001, 2992931569818, 6067876449637, 221436483756750, 448940843963137, 16383306866429682, 33215554576822501 (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 (0,74,0,-1).

FORMULA

G.f.: -(x^3-18*x^2-37*x-18)/(x^4-74*x^2+1). - Vincenzo Librandi, Nov 06 2013

a(n) = 74*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 06 2013

MATHEMATICA

Numerator[Convergents[Sqrt[342], 30]] (* or *) CoefficientList[Series[-(x^3 - 18 x^2 - 37 x - 18)/(x^4 - 74 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 06 2013 *)

LinearRecurrence[{0, 74, 0, -1}, {18, 37, 1350, 2737}, 30] (* Harvey P. Dale, Dec 28 2017 *)

PROG

(MAGMA) I:=[18, 37, 1350, 2737]; [n le 4 select I[n] else 74*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 06 2013

CROSSREFS

Cf. A041647.

Sequence in context: A041640 A041642 A041644 * A244412 A114698 A119127

Adjacent sequences:  A041643 A041644 A041645 * A041647 A041648 A041649

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 20 10:01 EDT 2019. Contains 326143 sequences. (Running on oeis4.)