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A042302 Numerators of continued fraction convergents to sqrt(678). 2
26, 677, 35230, 916657, 47701394, 1241152901, 64587652246, 1680520111297, 87451633439690, 2275422989543237, 118409447089688014, 3080921047321431601, 160326303907804131266, 4171564822650228844517, 217081697081719704046150 (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 (0,1354,0,-1).

FORMULA

G.f.: (26 +677*x +26*x^2 -x^3)/(1 -1354*x^2 +x^4). - Vincenzo Librandi, Nov 21 2013

a(n) = 1354*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 21 2013

MATHEMATICA

Numerator[Convergents[Sqrt[678], 20]] (* Harvey P. Dale, Oct 08 2012 *)

CoefficientList[Series[(26 + 677 x + 26 x^2 - x^3)/(1 - 1354 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)

PROG

(Magma) I:=[26, 677, 35230, 916657]; [n le 4 select I[n] else 1354*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

CROSSREFS

Cf. A042303.

Sequence in context: A188696 A009970 A041313 * A097835 A158643 A181227

Adjacent sequences:  A042299 A042300 A042301 * A042303 A042304 A042305

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 29 17:18 EDT 2022. Contains 357090 sequences. (Running on oeis4.)