A041601 Denominators of continued fraction convergents to sqrt(318).

1, 1, 5, 6, 209, 215, 1069, 1284, 44725, 46009, 228761, 274770, 9570941, 9845711, 48953785, 58799496, 2048136649, 2106936145, 10475881229, 12582817374, 438291671945, 450874489319, 2241789629221, 2692664118540, 93792369659581, 96485033778121

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,214,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+6*x^2+1) / (x^8-214*x^4+1). - Colin Barker, Nov 19 2013

a(n) = 214*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[318], 30]] (* Vincenzo Librandi Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 5, 6, 209, 215, 1069, 1284]; [n le 8 select I[n] else 214*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041600, A040300.

Sequence in context: A337465 A041411 A103089 * A301648 A041827 A042089

Adjacent sequences: A041598 A041599 A041600 * A041602 A041603 A041604

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved