A041723 Denominators of continued fraction convergents to sqrt(381).

1, 1, 2, 25, 27, 52, 2003, 2055, 4058, 50751, 54809, 105560, 4066089, 4171649, 8237738, 103024505, 111262243, 214286748, 8254158667, 8468445415, 16722604082, 209139694399, 225862298481, 435001992880, 16755938027921, 17190940020801, 33946878048722

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, 2030, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-26*x^3-1) / (x^12-2030*x^6+1). - Colin Barker, Nov 22 2013

a(n) = 2030*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 23 2013

Maple

convert(sqrt(381), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[381], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 1, 2, 25, 27, 52, 2003, 2055, 4058, 50751, 54809, 105560]; [n le 12 select I[n] else 2030*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041722, A040361.

Sequence in context: A092045 A317886 A054283 * A067443 A163497 A264118

Adjacent sequences: A041720 A041721 A041722 * A041724 A041725 A041726

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved