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 A042375 Denominators of continued fraction convergents to sqrt(714). 2
 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 (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 (0,0,0,0,0,0,0,0,0,8230,0,0,0,0,0,0,0,0,0,-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

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Last modified December 2 20:36 EST 2023. Contains 367526 sequences. (Running on oeis4.)