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A041880 Numerators of continued fraction convergents to sqrt(462). 2
21, 43, 1827, 3697, 157101, 317899, 13508859, 27335617, 1161604773, 2350545163, 99884501619, 202119548401, 8588905534461, 17379930617323, 738545991462027, 1494471913541377, 63506366360199861, 128507204633941099 (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 (0,86,0,-1).

FORMULA

G.f.: (21 +43*x +21*x^2 -x^3)/(1 -86*x^2 +x^4). - Vincenzo Librandi, Nov 11 2013

a(n) = 86*a(n-2) -a(n-4). - Vincenzo Librandi, Nov 11 2013

MATHEMATICA

Numerator[Convergents[Sqrt[462], 30]] (* or *) CoefficientList[Series[(21 + 43 x + 21 x^2 - x^3)/(1 - 86 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 11 2013 *)

LinearRecurrence[{0, 86, 0, -1}, {21, 43, 1827, 3697}, 30] (* Harvey P. Dale, Jul 25 2015 *)

PROG

(MAGMA) I:=[21, 43, 1827, 3697]; [n le 4 select I[n] else 86*Self(n-2)-Self(n-4): n in [1..20]]; // Vincenzo Librandi, Nov 11 2013

CROSSREFS

Cf. A041881.

Sequence in context: A041872 A041876 A041878 * A063319 A120071 A180863

Adjacent sequences:  A041877 A041878 A041879 * A041881 A041882 A041883

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)