A041336 Numerators of continued fraction convergents to sqrt(182).

13, 27, 715, 1457, 38597, 78651, 2083523, 4245697, 112471645, 229188987, 6071385307, 12371959601, 327742334933, 667856629467, 17692014701075, 36051886031617, 955041051523117, 1946133989077851, 51554524767547243, 105055183524172337, 2782989296396028005

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,54,0,-1).

Formula

G.f.: -(x+1)*(x^2-14*x-13) / (x^4-54*x^2+1). - Colin Barker, Nov 06 2013

a(0)=13, a(1)=27, a(2)=715, a(3)=1457, a(n)=54*a(n-2)-a(n-4). - Harvey P. Dale, Mar 27 2015

Mathematica

Numerator[Convergents[Sqrt[182], 30]] (* Vincenzo Librandi, Nov 01 2013 *)
LinearRecurrence[{0, 54, 0, -1}, {13, 27, 715, 1457}, 30] (* Harvey P. Dale, Mar 27 2015 *)

Crossrefs

Cf. A041337.

Sequence in context: A146372 A018946 A042397 * A145417 A157206 A138685

Adjacent sequences: A041333 A041334 A041335 * A041337 A041338 A041339

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 06 2013

Status

approved