A042078 Numerators of continued fraction convergents to sqrt(563).

23, 24, 71, 95, 261, 6098, 12457, 18555, 49567, 68122, 3183179, 3251301, 9685781, 12937082, 35559945, 830815817, 1697191579, 2528007396, 6753206371, 9281213767, 433689039653, 442970253420, 1319629546493, 1762599799913, 4844829146319

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, 0, 0, 0, 0, 136244, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (23 +24*x +71*x^2 +95*x^3 +261*x^4 +6098*x^5 +12457*x^6 +18555*x^7 +49567*x^8 +68122*x^9 +49567*x^10 -18555*x^11 +12457*x^12 -6098*x^13 +261*x^14 -95*x^15 +71*x^16 -24*x^17 +23*x^18 -x^19)/(1 -136244*x^10 +x^20). [Bruno Berselli, Nov 15 2013]

Mathematica

Numerator[Convergents[Sqrt[563], 30]] (* Vincenzo Librandi, Nov 15 2013 *)
CoefficientList[Series[(23 + 24 x + 71 x^2 + 95 x^3 + 261 x^4 + 6098 x^5 + 12457 x^6 + 18555 x^7 + 49567 x^8 + 68122 x^9 + 49567 x^10 - 18555 x^11 + 12457 x^12 - 6098 x^13 + 261 x^14 - 95 x^15 + 71 x^16 - 24 x^17 + 23 x^18 - x^19)/(1 - 136244 x^10 + x^20), {x, 0, 30}], x] (* Bruno Berselli, Nov 15 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 136244, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {23, 24, 71, 95, 261, 6098, 12457, 18555, 49567, 68122, 3183179, 3251301, 9685781, 12937082, 35559945, 830815817, 1697191579, 2528007396, 6753206371, 9281213767}, 20] (* Harvey P. Dale, Aug 10 2020 *)

Crossrefs

Cf. A042079.

Sequence in context: A042060 A042058 A045859 * A042080 A042076 A042074

Adjacent sequences: A042075 A042076 A042077 * A042079 A042080 A042081

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved