A041735 Denominators of continued fraction convergents to sqrt(387).

1, 1, 3, 58, 119, 177, 6845, 7022, 20889, 403913, 828715, 1232628, 47668579, 48901207, 145470993, 2812850074, 5771171141, 8584021215, 331963977311, 340547998526, 1013059974363, 19588687511423, 40190434997209, 59779122508632, 2311797090325225

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, 6964, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10-x^9+3*x^8-58*x^7+119*x^6-177*x^5-119*x^4-58*x^3-3*x^2-x-1) / (x^12-6964*x^6+1). - Colin Barker, Nov 23 2013

a(n) = 6964*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[387], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 1, 3, 58, 119, 177, 6845, 7022, 20889, 403913, 828715, 1232628]; [n le 12 select I[n] else 6964*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041734, A040367.

Sequence in context: A198915 A037107 A335293 * A156487 A254653 A243510

Adjacent sequences: A041732 A041733 A041734 * A041736 A041737 A041738

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved