A042916 Numerators of continued fraction convergents to sqrt(990).

31, 63, 409, 881, 55031, 110943, 720689, 1552321, 96964591, 195481503, 1269853609, 2735188721, 170851554311, 344438297343, 2237481338369, 4819400974081, 301040341731391, 606900084436863, 3942440848352569, 8491781781142001, 530432911279156631

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1762,0,0,0,-1).

Formula

G.f.: (31 + 63*x + 409*x^2 + 881*x^3 +409*x^4 -63*x^5 +31*x^6 -x^7)/(1 -1762*x^4 +x^8). - Vincenzo Librandi, Dec 09 2013

a(n) = 1762*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 09 2013

Mathematica

Numerator[Convergents[Sqrt[990], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 409 x^2 + 881 x^3 + 409 x^4 - 63 x^5 + 31 x^6 - x^7)/(1 - 1762 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)
LinearRecurrence[{0, 0, 0, 1762, 0, 0, 0, -1}, {31, 63, 409, 881, 55031, 110943, 720689, 1552321}, 30] (* Harvey P. Dale, Jun 07 2020 *)

Prog

(Magma) I:=[31, 63, 409, 881, 55031, 110943, 720689, 1552321]; [n le 8 select I[n] else 1762*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

Crossrefs

Cf. A042917.

Sequence in context: A167783 A326381 A042914 * A042918 A042920 A247438

Adjacent sequences: A042913 A042914 A042915 * A042917 A042918 A042919

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved