A041794 Numerators of continued fraction convergents to sqrt(418).

20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897, 92724030452, 187740653801, 843686645656, 17061473566921, 69089580913340, 155240635393601, 6278714996657380

Offset

0,1

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, 67714, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^11-20*x^10+41*x^9-184*x^8+3721*x^7-15068*x^6-33857*x^5-15068*x^4-3721*x^3-184*x^2-41*x-20)/(x^12-67714*x^6+1). - Vincenzo Librandi, Nov 09 2013

a(n) = 67714*a(n-6)-a(n-12). - Vincenzo Librandi, Nov 09 2013

Mathematica

Numerator/@Convergents[Sqrt[418], 30]  (* Harvey P. Dale, Apr 07 2011 *)
CoefficientList[Series[-(x^11 - 20 x^10 + 41 x^9 - 184 x^8 + 3721 x^7 - 15068 x^6 - 33857 x^5 - 15068 x^4 - 3721 x^3 - 184 x^2 - 41 x - 20)/(x^12 - 67714 x^6 + 1), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 67714, 0, 0, 0, 0, 0, -1}, {20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897}, 30] (* Vincenzo Librandi, Nov 09 2013 *)

Prog

(Magma) I:=[20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897]; [n le 12 select I[n] else 67714*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 09 2013

Crossrefs

Cf. A041795.

Sequence in context: A171389 A038639 A041792 * A041796 A041798 A132762

Adjacent sequences: A041791 A041792 A041793 * A041795 A041796 A041797

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved