A041253 Denominators of continued fraction convergents to sqrt(138).

1, 1, 3, 4, 91, 95, 281, 376, 8553, 8929, 26411, 35340, 803891, 839231, 2482353, 3321584, 75557201, 78878785, 233314771, 312193556, 7101573003, 7413766559, 21929106121, 29342872680, 667472305081, 696815177761, 2061102660603, 2757917838364, 62735295104611

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,94,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-94*x^4+1). - Colin Barker, Nov 14 2013

a(n) = 94*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[138], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[1, 1, 3, 4, 91, 95, 281, 376]; [n le 8 select I[n] else 94*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041252, A010197.

Sequence in context: A111799 A135237 A316197 * A297119 A156182 A126578

Adjacent sequences: A041250 A041251 A041252 * A041254 A041255 A041256

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved