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A041593 Denominators of continued fraction convergents to sqrt(314). 2
1, 1, 3, 4, 7, 18, 25, 868, 893, 2654, 3547, 6201, 15949, 22150, 769049, 791199, 2351447, 3142646, 5494093, 14130832, 19624925, 681378282, 701003207, 2083384696, 2784387903, 4867772599, 12519933101, 17387705700, 603701926901, 621089632601, 1845881192103 (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 (0,0,0,0,0,0,886,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^12-x^11+3*x^10-4*x^9+7*x^8-18*x^7+25*x^6+18*x^5+7*x^4+4*x^3+3*x^2+x+1) / (x^14+886*x^7-1). - Colin Barker, Nov 19 2013

a(n) = 886*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 21 2013

MATHEMATICA

Denominator[Convergents[Sqrt[314], 30]] (* Harvey P. Dale, Aug 08 2013 *)

CoefficientList[Series[-(x^12 - x^11 + 3 x^10 - 4 x^9 + 7 x^8 - 18 x^7 + 25 x^6 + 18 x^5 + 7 x^4 + 4 x^3 + 3 x^2 + x + 1)/(x^14 + 886 x^7 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 21 2013 *)

PROG

(MAGMA) I:=[1, 1, 3, 4, 7, 18, 25, 868, 893, 2654, 3547, 6201, 15949, 22150]; [n le 14 select I[n] else 886*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

CROSSREFS

Cf. A041592, A040296.

Sequence in context: A093611 A042375 A153067 * A258740 A109749 A041497

Adjacent sequences:  A041590 A041591 A041592 * A041594 A041595 A041596

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 19 2013

STATUS

approved

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Last modified February 15 21:12 EST 2019. Contains 320138 sequences. (Running on oeis4.)