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A041131
Denominators of continued fraction convergents to sqrt(74).
2
1, 1, 2, 3, 5, 83, 88, 171, 259, 430, 7139, 7569, 14708, 22277, 36985, 614037, 651022, 1265059, 1916081, 3181140, 52814321, 55995461, 108809782, 164805243, 273615025, 4542645643, 4816260668, 9358906311, 14175166979, 23534073290, 390720339619, 414254412909
OFFSET
0,3
LINKS
FORMULA
G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+86*x^5-1). - Colin Barker, Nov 13 2013
a(n) = 86*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 11 2013
MATHEMATICA
Denominator/@Convergents[Sqrt[74], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^4 - 3 x^3 + 4 x^2 - 2 x + 1) (x^4 + 2 x^3 + 4 x^2 + 3 x + 1)/(x^10 + 86 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0, 0, 0, 0, 86, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 83, 88, 171, 259, 430}, 50] (* Harvey P. Dale, Nov 09 2017 *)
PROG
(Magma) I:=[1, 1, 2, 3, 5, 83, 88, 171, 259, 430]; [n le 10 select I[n] else 86*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved