A041592 Numerators of continued fraction convergents to sqrt(314).

17, 18, 53, 71, 124, 319, 443, 15381, 15824, 47029, 62853, 109882, 282617, 392499, 13627583, 14020082, 41667747, 55687829, 97355576, 250398981, 347754557, 12074053919, 12421808476, 36917670871, 49339479347, 86257150218, 221853779783, 308110930001

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,886,0,0,0,0,0,0,1).

Formula

G.f.: -(x^13 -17*x^12 +18*x^11 -53*x^10 +71*x^9 -124*x^8 +319*x^7 +443*x^6 +319*x^5 +124*x^4 +71*x^3 +53*x^2 +18*x +17) / (x^14 +886*x^7 -1). - Colin Barker, Nov 09 2013

Mathematica

Numerator[Convergents[Sqrt[314], 30]] (* Vincenzo Librandi, Nov 04 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 886, 0, 0, 0, 0, 0, 0, 1}, {17, 18, 53, 71, 124, 319, 443, 15381, 15824, 47029, 62853, 109882, 282617, 392499}, 30] (* Harvey P. Dale, Oct 19 2016 *)

Crossrefs

Cf. A041593.

Sequence in context: A041582 A041580 A041578 * A041594 A041590 A041596

Adjacent sequences: A041589 A041590 A041591 * A041593 A041594 A041595

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 09 2013

Status

approved