A041139 Denominators of continued fraction convergents to sqrt(78).
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,106,0,0,0,-1).
Programs
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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
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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 *)
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