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
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).
Programs
-
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
-
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 *)
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
Extensions
More terms from Colin Barker, Nov 17 2013
Comments