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A041413
Denominators of continued fraction convergents to sqrt(221).
2
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
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
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 17 2013
STATUS
approved