A042375 Denominators of continued fraction convergents to sqrt(714).

1, 1, 3, 4, 7, 18, 25, 43, 111, 154, 8119, 8273, 24665, 32938, 57603, 148144, 205747, 353891, 913529, 1267420, 66819369, 68086789, 202992947, 271079736, 474072683, 1219225102, 1693297785, 2912522887, 7518343559, 10430866446, 549923398751, 560354265197

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,8230,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -x^17 +3*x^16 -4*x^15 +7*x^14 -18*x^13 +25*x^12 -43*x^11 +111*x^10 -154*x^9 -111*x^8 -43*x^7 -25*x^6 -18*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1) / (x^20 -8230*x^10 +1). - Colin Barker, Dec 09 2013

a(n) = 8230*a(n-10) - a(n-20). - Wesley Ivan Hurt, Sep 07 2022

Mathematica

Denominator/@Convergents[Sqrt[714], 50]  (* Harvey P. Dale, Mar 15 2011 *)
CoefficientList[Series[-(x^18 - x^17 + 3 x^16 - 4 x^15 + 7 x^14 - 18 x^13 + 25 x^12 - 43 x^11 + 111 x^10 - 154 x^9 - 111 x^8 - 43 x^7 - 25 x^6 - 18 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^20 - 8230 x^10 + 1), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 21 2014 *)

Crossrefs

Cf. A042374, A040687.

Sequence in context: A327318 A344783 A093611 * A153067 A041593 A258740

Adjacent sequences: A042372 A042373 A042374 * A042376 A042377 A042378

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 09 2013

Status

approved