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A041257 Denominators of continued fraction convergents to sqrt(140). 2
1, 1, 5, 6, 137, 143, 709, 852, 19453, 20305, 100673, 120978, 2762189, 2883167, 14294857, 17178024, 392211385, 409389409, 2029769021, 2439158430, 55691254481, 58130412911, 288212906125, 346343319036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,142,0,0,0,-1).

FORMULA

G.f.: (1 +x +5*x^2 +6*x^3 -5*x^4 +x^5 -x^6)/(1 -142*x^4 +x^8). - Vincenzo Librandi, Dec 13 2013

a(n) = 142*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013

MATHEMATICA

Denominator[Convergents[Sqrt[140], 30]] (* or *) CoefficientList[Series[(1 + x + 5 x^2 + 6 x^3 - 5 x^4 + x^5 - x^6)/(1 - 142 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 13 2013 *)

PROG

(MAGMA) I:=[1, 1, 5, 6, 137, 143, 709, 852]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

CROSSREFS

Cf. A041256.

Sequence in context: A065354 A078984 A266718 * A041411 A103089 A041601

Adjacent sequences:  A041254 A041255 A041256 * A041258 A041259 A041260

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 25 21:00 EST 2020. Contains 332258 sequences. (Running on oeis4.)