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A041762 Numerators of continued fraction convergents to sqrt(402). 2
20, 401, 16060, 321601, 12880100, 257923601, 10329824140, 206854406401, 8284506080180, 165896976010001, 6644163546480220, 133049167905614401, 5328610879771056260, 106705266763326739601, 4273539281412840640300, 85577490895020139545601 (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 (0,802,0,-1).

FORMULA

G.f.: -(x^3-20*x^2-401*x-20) / (x^4-802*x^2+1). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

a(n) = 802*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 08 2013, simplified by Colin Barker, Dec 28 2013

MATHEMATICA

Numerator[Convergents[Sqrt[402], 30]] (* Harvey P. Dale, Apr 29 2013 *)

CoefficientList[Series[(20 + 401 x + 16060 x^2 + 321601 x^3 + 16060 x^4 - 401 x^5 + 20 x^6 - x^7)/(1 - 643202 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 08 2013 *)

PROG

(MAGMA) I:=[20, 401, 16060, 321601, 12880100, 257923601, 10329824140, 206854406401]; [n le 8 select I[n] else 643202*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 08 2013

CROSSREFS

Cf. A041763, A040381.

Sequence in context: A055476 A223180 A041181 * A196740 A196898 A068772

Adjacent sequences:  A041759 A041760 A041761 * A041763 A041764 A041765

KEYWORD

nonn,frac,easy,less

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Dec 28 2013

STATUS

approved

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Last modified October 20 17:24 EDT 2018. Contains 316392 sequences. (Running on oeis4.)