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A041139 - OEIS
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A041139
Denominators of continued fraction convergents to sqrt(78).
2
1, 1, 5, 6, 101, 107, 529, 636, 10705, 11341, 56069, 67410, 1134629, 1202039, 5942785, 7144824, 120259969, 127404793, 629879141, 757283934, 12746422085, 13503706019, 66761246161, 80264952180, 1351000481041, 1431265433221, 7076062213925, 8507327647146
OFFSET
0,3
FORMULA
G.f.: -(x^2-x-1)*(x^4+6*x^2+1) / (x^8-106*x^4+1). - Colin Barker, Nov 13 2013
a(n) = 106*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[78], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^2 - x - 1) (x^4 + 6*x^2 + 1)/(x^8 - 106 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 106, 0, 0, 0, -1}, {1, 1, 5, 6, 101, 107, 529, 636}, 30] (* Harvey P. Dale, Sep 15 2018 *)
PROG
(Magma) I:=[1, 1, 5, 6, 101, 107, 529, 636]; [n le 8 select I[n] else 106*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved