A041741 Denominators of continued fraction convergents to sqrt(390).

1, 1, 3, 4, 155, 159, 473, 632, 24489, 25121, 74731, 99852, 3869107, 3968959, 11807025, 15775984, 611294417, 627070401, 1865435219, 2492505620, 96580648779, 99073154399, 294726957577, 393800111976, 15259131212665, 15652931324641, 46564993861947

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,158,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-158*x^4+1). - Colin Barker, Nov 23 2013

a(n) = 158*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[390], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 158, 0, 0, 0, -1}, {1, 1, 3, 4, 155, 159, 473, 632}, 30] (* Harvey P. Dale, Aug 06 2015 *)

Prog

(Magma) I:=[1, 1, 3, 4, 155, 159, 473, 632]; [n le 8 select I[n] else 158*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041740, A040370.

Sequence in context: A077032 A370385 A041595 * A041903 A156513 A082213

Adjacent sequences: A041738 A041739 A041740 * A041742 A041743 A041744

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved