A041593 Denominators of continued fraction convergents to sqrt(314).

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

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 A307738

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