A040206 -id:A040206 - cp's OEIS frontend

A177157 Decimal expansion of sqrt(221).

1, 4, 8, 6, 6, 0, 6, 8, 7, 4, 7, 3, 1, 8, 5, 0, 5, 5, 2, 2, 6, 1, 2, 0, 0, 8, 2, 1, 3, 9, 3, 1, 3, 9, 6, 6, 5, 1, 4, 4, 8, 9, 8, 5, 5, 1, 3, 7, 2, 0, 8, 6, 1, 5, 6, 0, 5, 6, 3, 0, 9, 4, 8, 1, 0, 2, 5, 1, 8, 3, 7, 3, 1, 4, 7, 8, 1, 1, 6, 7, 6, 5, 8, 6, 1, 5, 8, 3, 6, 4, 6, 0, 2, 7, 3, 9, 6, 1, 1, 0, 0, 7, 2, 4, 1

Offset: 2

Klaus Brockhaus, May 03 2010

Continued fraction expansion of sqrt(221) is A040206.

			sqrt(221) = 14.86606874731850552261...

Cf. A010470 (decimal expansion of sqrt(13)), A010473 (decimal expansion of sqrt(17)), A177156 (decimal expansion of (9+sqrt(221))/14), A040206 (14 followed by (repeat 1, 6, 2, 6, 1, 28)).

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

Original entry on oeis.org

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

N. J. A. Sloane

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).

Cf. A041412, A040206, A177157.

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

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 *)

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

More terms from Colin Barker, Nov 17 2013

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A177157 Decimal expansion of sqrt(221).

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

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