A041445 Denominators of continued fraction convergents to sqrt(238).

1, 2, 5, 7, 103, 110, 323, 756, 23003, 46762, 116527, 163289, 2402573, 2565862, 7534297, 17634456, 536567977, 1090770410, 2718108797, 3808879207, 56042417695, 59851296902, 175745011499, 411341319900, 12515984608499, 25443310536898, 63402605682295

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,23326,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +103*x^10 -110*x^9 +323*x^8 -756*x^7 -323*x^6 -110*x^5 -103*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -23326*x^8 +1). - Colin Barker, Nov 17 2013

a(n) = 23326*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 18 2013

Mathematica

Denominator[Convergents[Sqrt[238], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

Prog

(Magma) I:=[1, 2, 5, 7, 103, 110, 323, 756, 23003, 46762, 116527, 163289, 2402573, 2565862, 7534297, 17634456]; [n le 16 select I[n] else 23326*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013

Crossrefs

Cf. A041444, A040222.

Sequence in context: A343833 A103056 A381903 * A265815 A041961 A242169

Adjacent sequences: A041442 A041443 A041444 * A041446 A041447 A041448

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved