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A041141 - OEIS
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A041141
Denominators of continued fraction convergents to sqrt(79).
2
1, 1, 8, 9, 152, 161, 1279, 1440, 24319, 25759, 204632, 230391, 3890888, 4121279, 32739841, 36861120, 622517761, 659378881, 5238169928, 5897548809, 99598950872, 105496499681, 838074448639, 943570948320, 15935209621759, 16878780570079
OFFSET
0,3
FORMULA
G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-160*x^4+1). - Colin Barker, Nov 13 2013
a(n) = 160*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[79], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 9 x^2 + 1)/(x^8 - 160 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 160, 0, 0, 0, -1}, {1, 1, 8, 9, 152, 161, 1279, 1440}, 40] (* Harvey P. Dale, Aug 09 2021 *)
PROG
(Magma) I:=[1, 1, 8, 9, 152, 161, 1279, 1440]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved