A042650 Numerators of continued fraction convergents to sqrt(855).

29, 117, 731, 3041, 177109, 711477, 4445971, 18495361, 1077176909, 4327202997, 27040394891, 112488782561, 6551389783429, 26318047916277, 164459677281091, 684156757040641, 39845551585638269, 160066363099593717

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 6082, 0, 0, 0, -1).

Formula

G.f.: (29 +117*x +731*x^2 +3041*x^3 +731*x^4 -117*x^5 +29*x^6 -x^7)/(1 -6082*x^4 +x^8). - Vincenzo Librandi, Nov 30 2013

a(n) = 6082*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 30 2013

Mathematica

Numerator[Convergents[Sqrt[855], 30]] (* or *) CoefficientList[Series[(29 + 117 x + 731 x^2 + 3041 x^3 + 731 x^4 - 117 x^5 + 29 x^6 - x^7)/(1 - 6082 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 30 2013 *)
LinearRecurrence[{0, 0, 0, 6082, 0, 0, 0, -1}, {29, 117, 731, 3041, 177109, 711477, 4445971, 18495361}, 20] (* Harvey P. Dale, Oct 22 2017 *)

Prog

(Magma) I:=[29, 117, 731, 3041, 177109, 711477, 4445971, 18495361]; [n le 8 select I[n] else 6082*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 30 2013

Crossrefs

Cf. A042651.

Sequence in context: A188359 A042648 A233046 * A158560 A330811 A118614

Adjacent sequences: A042647 A042648 A042649 * A042651 A042652 A042653

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved