A042467 Denominators of continued fraction convergents to sqrt(761).

1, 1, 2, 5, 12, 17, 29, 1583, 1612, 3195, 8002, 19199, 27201, 46400, 2532801, 2579201, 5112002, 12803205, 30718412, 43521617, 74240029, 4052483183, 4126723212, 8179206395, 20485136002, 49149478399, 69634614401, 118784092800, 6483975625601, 6602759718401

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1600,0,0,0,0,0,0,1).

Formula

G.f.: -(x^12 - x^11 + 2*x^10 - 5*x^9 + 12*x^8 - 17*x^7 + 29*x^6 + 17*x^5 + 12*x^4 + 5*x^3 + 2*x^2 + x + 1) / (x^14 + 1600*x^7 - 1). - Colin Barker, Dec 14 2013

a(n) = 1600*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 14 2013

Mathematica

Denominator[Convergents[Sqrt[761], 30]] (* Vincenzo Librandi, Dec 14 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 2, 5, 12, 17, 29, 1583, 1612, 3195, 8002, 19199, 27201, 46400}, 30] (* Harvey P. Dale, Aug 23 2015 *)

Prog

(Magma) I:=[1, 1, 2, 5, 12, 17, 29, 1583, 1612, 3195, 8002, 19199, 27201, 46400]; [n le 14 select I[n] else 1600*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 14 2013

Crossrefs

Cf. A042466, A040733.

Sequence in context: A066267 A084122 A042143 * A024465 A041889 A055906

Adjacent sequences: A042464 A042465 A042466 * A042468 A042469 A042470

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 14 2013

Status

approved