A041413 Denominators of continued fraction convergents to sqrt(221).

1, 1, 7, 15, 97, 112, 3233, 3345, 23303, 49951, 323009, 372960, 10765889, 11138849, 77598983, 166336815, 1075619873, 1241956688, 35850407137, 37092363825, 258404590087, 553901543999, 3581813854081, 4135715398080, 119381845000321, 123517560398401

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3330,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -x^9 +7*x^8 -15*x^7 +97*x^6 -112*x^5 -97*x^4 -15*x^3 -7*x^2 -x -1) / ((x^4 -15*x^2 +1)*(x^8 +15*x^6 +224*x^4 +15*x^2 +1)). - Colin Barker, Nov 17 2013

a(n) = 3330*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 17 2013

Mathematica

Denominator/@Convergents[Sqrt[221], 30]  (* Harvey P. Dale, Apr 02 2011 *)
CoefficientList[Series[-(x^10 - x^9 + 7 x^8 - 15 x^7 + 97 x^6 - 112 x^5 - 97 x^4 - 15 x^3 - 7 x^2 - x - 1)/((x^4 - 15 x^2 + 1) (x^8 + 15 x^6 + 224 x^4 + 15 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)

Prog

(Magma) I:=[1, 1, 7, 15, 97, 112, 3233, 3345, 23303, 49951, 323009, 372960]; [n le 12 select I[n] else 3330*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013

Crossrefs

Cf. A041412, A040206, A177157.

Sequence in context: A177177 A335758 A343279 * A144536 A231399 A231466

Adjacent sequences: A041410 A041411 A041412 * A041414 A041415 A041416

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 17 2013

Status

approved