A042265 Denominators of continued fraction convergents to sqrt(658).

1, 1, 2, 3, 20, 23, 43, 66, 3343, 3409, 6752, 10161, 67718, 77879, 145597, 223476, 11319397, 11542873, 22862270, 34405143, 229293128, 263698271, 492991399, 756689670, 38327474899, 39084164569, 77411639468, 116495804037, 776386463690, 892882267727

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, 0, 0, 0, 0, 3386, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+22*x^4+1) / (x^16-3386*x^8+1). - Colin Barker, Dec 06 2013

a(n) = 3386*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Jan 19 2014

Maple

convert(sqrt(658), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 07 2013

Mathematica

Denominator[Convergents[Sqrt[658], 30]] (* Vincenzo Librandi, Jan 19 2014 *)

Prog

(Magma) I:=[1, 1, 2, 3, 20, 23, 43, 66, 3343, 3409, 6752, 10161, 67718, 77879, 145597, 223476]; [n le 16 select I[n] else 3386*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042264, A040632.

Sequence in context: A032809 A279180 A279471 * A041093 A154746 A042781

Adjacent sequences: A042262 A042263 A042264 * A042266 A042267 A042268

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 06 2013

Status

approved