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

0,3

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A041170.

Sequence in context: A318208 A341851 A132414 * A279935 A111799 A135237

Adjacent sequences: A041168 A041169 A041170 * A041172 A041173 A041174

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 12 2013

Status

approved