A041256 Numerators of continued fraction convergents to sqrt(140).

11, 12, 59, 71, 1621, 1692, 8389, 10081, 230171, 240252, 1191179, 1431431, 32682661, 34114092, 169139029, 203253121, 4640707691, 4843960812, 24016550939, 28860511751, 658947809461, 687808321212

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,142,0,0,0,-1).

Formula

G.f.: (11 +12*x +59*x^2 +71x^3 +59x^4 -12x^5 +11x^6 -x^7) / ((1 -12*x^2 +x^4)*(1 +12*x^2 +x^4)). - Vincenzo Librandi, Nov 01 2013

a(n) = 142*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 01 2013

Mathematica

Numerator[Convergents[Sqrt[140], 30]] (* or *) CoefficientList[Series[(11 + 12 x + 59 x^2 + 71 x^3 + 59 x^4 - 12 x^5 + 11 x^6 - x^7)/(1 - 142 x^4 + x^8), {x, 0, 25}], x] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 142, 0, 0, 0, -1}, {11, 12, 59, 71, 1621, 1692, 8389, 10081}, 30] (* Harvey P. Dale, Feb 23 2015 *)

Prog

(Magma) I:=[11, 12, 59, 71, 1621, 1692, 8389, 10081]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013

Crossrefs

Cf. A041257.

Sequence in context: A248323 A291059 A041254 * A059181 A041258 A082262

Adjacent sequences: A041253 A041254 A041255 * A041257 A041258 A041259

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved