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A041758 Numerators of continued fraction convergents to sqrt(399). 3
19, 20, 779, 799, 31141, 31940, 1244861, 1276801, 49763299, 51040100, 1989287099, 2040327199, 79521720661, 81562047860, 3178879539341, 3260441587201, 127075659852979, 130336101440180, 5079847514579819, 5210183616019999, 203066824923339781 (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 (0,40,0,-1).

FORMULA

G.f.: (19 + 20*x + 19*x^2 - x^3)/(1 - 40*x^2 + x^4). - Vincenzo Librandi, Mov 07 2013

a(n) = 40*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 07 2013

MATHEMATICA

Numerator[Convergents[Sqrt[399], 30]] (* or *) CoefficientList[Series[(19 + 20 x + 19 x^2 - x^3)/(1 - 40 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Mov 07 2013 *)

LinearRecurrence[{0, 40, 0, -1}, {19, 20, 779, 799}, 30] (* Harvey P. Dale, Sep 21 2018 *)

PROG

(MAGMA) I:=[19, 20, 779, 799]; [n le 4 select I[n] else 40*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 07 2013

CROSSREFS

Cf. A041759.

Sequence in context: A041179 A041756 A041757 * A042735 A156758 A089837

Adjacent sequences:  A041755 A041756 A041757 * A041759 A041760 A041761

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 18 17:21 EST 2019. Contains 329287 sequences. (Running on oeis4.)