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A042078 Numerators of continued fraction convergents to sqrt(563). 2
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified March 21 22:19 EDT 2019. Contains 321382 sequences. (Running on oeis4.)