A041721 Denominators of continued fraction convergents to sqrt(380).

1, 2, 77, 156, 6005, 12166, 468313, 948792, 36522409, 73993610, 2848279589, 5770552788, 222129285533, 450029123854, 17323235991985, 35096501107824, 1350990278089297, 2737077057286418, 105359918454973181, 213456913967232780, 8216722649209818821

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, 78, 0, -1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-78*x^2+1). - Colin Barker, Nov 22 2013

a(n) = 78*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 23 2013

Maple

convert(sqrt(380), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[380], 30]] (* Harvey P. Dale, May 29 2013 *)
CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 78 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 2, 77, 156]; [n le 4 select I[n] else 78*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041720, A040360.

Sequence in context: A349066 A266877 A301472 * A048358 A124456 A338588

Adjacent sequences: A041718 A041719 A041720 * A041722 A041723 A041724

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved