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A041944 Numerators of continued fraction convergents to sqrt(495). 2
22, 89, 3938, 15841, 700942, 2819609, 124763738, 501874561, 22207244422, 89330852249, 3952764743378, 15900389825761, 703569917076862, 2830180058133209, 125231492474938058, 503756149957885441 (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 (0,178,0,-1).

FORMULA

G.f.: (22 + 89*x + 22*x^2 - x^3)/(1 - 178*x^2 + x^4). - Vincenzo Librandi, Nov 12 2013

a(n) = 178*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 12 2013

MATHEMATICA

Numerator[Convergents[Sqrt[495], 30]] (* or *) CoefficientList[Series[(22 + 89 x + 22 x^2 - x^3)/(1 - 178 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 12 2013 *)

LinearRecurrence[{0, 178, 0, -1}, {22, 89, 3938, 15841}, 30] (* Harvey P. Dale, Dec 07 2015 *)

PROG

(MAGMA) I:=[22, 89, 3938, 15841]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 12 2013

CROSSREFS

Cf. A041945.

Sequence in context: A041940 A041942 A231265 * A230357 A145769 A256152

Adjacent sequences:  A041941 A041942 A041943 * A041945 A041946 A041947

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 3 08:53 EDT 2020. Contains 336197 sequences. (Running on oeis4.)