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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
OFFSET
0,1
LINKS
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
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved