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A042080
Numerators of continued fraction convergents to sqrt(564).
2
23, 24, 71, 95, 4441, 4536, 13513, 18049, 843767, 861816, 2567399, 3429215, 160311289, 163740504, 487792297, 651532801, 30458301143, 31109833944, 92677969031, 123787802975, 5786916905881, 5910704708856
OFFSET
0,1
FORMULA
G.f.: -(x^7 - 23*x^6 + 24*x^5 - 71*x^4 - 95*x^3 - 71*x^2 -24*x - 23)/(x^8 - 190*x^4 + 1). - Vincenzo Librandi, Nov 16 2013
a(n) = 190*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013
MATHEMATICA
Numerator[Convergents[Sqrt[564], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 71 x^4 - 95 x^3 - 71 x^2 - 24 x - 23)/(x^8 - 190 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{0, 0, 0, 190, 0, 0, 0, -1}, {23, 24, 71, 95, 4441, 4536, 13513, 18049}, 30] (* Harvey P. Dale, Apr 18 2015 *)
PROG
(Magma) I:=[23, 24, 71, 95, 4441, 4536, 13513, 18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013
CROSSREFS
Cf. A042081.
Sequence in context: A042058 A045859 A042078 * A042076 A042074 A214510
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved