A042533 Denominators of continued fraction convergents to sqrt(795).

1, 5, 46, 235, 13206, 66265, 609591, 3114220, 175005911, 878143775, 8078299886, 41269643205, 2319178319366, 11637161240035, 107053629479681, 546905308638440, 30733750913232321, 154215659874800045, 1418674689786432726, 7247589108806963675

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, 13252, 0, 0, 0, -1).

Formula

G.f.: -(x^2 -5*x -1)*(x^4 +47*x^2 +1) / (x^8 -13252*x^4 +1). - Colin Barker, Dec 17 2013

a(n) = 13252*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 23 2014

Mathematica

Denominator[Convergents[Sqrt[795], 30]] (* Harvey P. Dale, Nov 12 2011 *)
CoefficientList[Series[-(x^2 - 5 x - 1) (x^4 + 47 x^2 + 1)/(x^8 - 13252 x^4 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Jan 23 2014 *)

Prog

(Magma) I:=[1, 5, 46, 235, 13206, 66265, 609591, 3114220]; [n le 8 select I[n] else 13252*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Jan 23 2014

Crossrefs

Cf. A042532, A040766.

Sequence in context: A318550 A318212 A096947 * A355056 A309185 A169963

Adjacent sequences: A042530 A042531 A042532 * A042534 A042535 A042536

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 17 2013

Status

approved