A041697 Denominators of continued fraction convergents to sqrt(368).

1, 5, 11, 60, 2291, 11515, 25321, 138120, 5273881, 26507525, 58288931, 317952180, 12140471771, 61020311035, 134181093841, 731925780240, 27947360742961, 140468729495045, 308884819733051, 1684892828160300, 64334812289824451, 323358954277282555

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2302,0,0,0,-1).

Formula

G.f.: -(x^2-5*x-1)*(x^4+12*x^2+1) / ((x^4-48*x^2+1)*(x^4+48*x^2+1)). - Colin Barker, Nov 22 2013

a(n) = 2302*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[368], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 2302, 0, 0, 0, -1}, {1, 5, 11, 60, 2291, 11515, 25321, 138120}, 30] (* Harvey P. Dale, Nov 21 2015 *)

Prog

(Magma) I:=[1, 5, 11, 60, 2291, 11515, 25321, 138120]; [n le 8 select I[n] else 2302*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041696, A040348.

Sequence in context: A173875 A095150 A215759 * A121170 A239322 A101209

Adjacent sequences: A041694 A041695 A041696 * A041698 A041699 A041700

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved