A041171 Denominators of continued fraction convergents to sqrt(95).
1, 1, 3, 4, 75, 79, 233, 312, 5849, 6161, 18171, 24332, 456147, 480479, 1417105, 1897584, 35573617, 37471201, 110516019, 147987220, 2774285979, 2922273199, 8618832377, 11541105576, 216358732745, 227899838321, 672158409387, 900058247708, 16873206868131, 17773265115839
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,78,0,0,0,-1).
Crossrefs
Cf. A041170.
Programs
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Magma
I:=[1, 1, 3, 4, 75, 79, 233, 312]; [n le 8 select I[n] else 78*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator[Convergents[Sqrt[95], 30]] (* or *) CoefficientList[Series[(1 + x + 3 x^2 + 4 x^3 - 3 x^4 + x^5 - x^6)/(1 - 78 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *) LinearRecurrence[{0,0,0,78,0,0,0,-1},{1,1,3,4,75,79,233,312},30] (* Harvey P. Dale, Mar 12 2016 *)
Formula
G.f.: (1 +x +3*x^2 +4*x^3 -3*x^4 +x^5 -x^6)/(1 -78*x^4 +x^8). - Vincenzo Librandi, Dec 12 2013
a(n) = 78*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 12 2013
Extensions
More terms from Vincenzo Librandi, Dec 12 2013