A041523 Denominators of continued fraction convergents to sqrt(278).

1, 1, 3, 49, 101, 150, 4901, 5051, 15003, 245099, 505201, 750300, 24514801, 25265101, 75045003, 1225985149, 2527015301, 3753000450, 122623029701, 126376030151, 375375090003, 6132377470199, 12640130030401, 18772507500600, 613360370049601, 632132877550201

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,5002,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-x^9+3*x^8-49*x^7+101*x^6-150*x^5-101*x^4-49*x^3-3*x^2-x-1) / (x^12-5002*x^6+1). - Colin Barker, Nov 18 2013

a(n) = 5002*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator/@Convergents[Sqrt[278], 50]  (* Harvey P. Dale, Mar 13 2011 *)
CoefficientList[Series[-(x^10 - x^9 + 3 x^8 - 49 x^7 + 101 x^6 - 150 x^5 - 101 x^4 - 49 x^3 - 3 x^2 - x - 1)/(x^12 - 5002 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 3, 49, 101, 150, 4901, 5051, 15003, 245099, 505201, 750300]; [n le 12 select I[n] else 5002*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041522, A040261.

Sequence in context: A188380 A252171 A160763 * A054206 A063777 A359886

Adjacent sequences: A041520 A041521 A041522 * A041524 A041525 A041526

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved