A041249 Denominators of continued fraction convergents to sqrt(136).

1, 1, 2, 3, 68, 71, 139, 210, 4759, 4969, 9728, 14697, 333062, 347759, 680821, 1028580, 23309581, 24338161, 47647742, 71985903, 1631337608, 1703323511, 3334661119, 5037984630, 114170322979, 119208307609, 233378630588, 352586938197, 7990291270922

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,70,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-70*x^4+1). - Colin Barker, Nov 14 2013

a(n) = 70*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[136], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 68, 71, 139, 210]; [n le 8 select I[n] else 70*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041248, A010195.

Sequence in context: A365289 A352163 A365504 * A356795 A360817 A184949

Adjacent sequences: A041246 A041247 A041248 * A041250 A041251 A041252

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved