A042746 Numerators of continued fraction convergents to sqrt(904).

30, 451, 27090, 406801, 24435150, 366934051, 22040478210, 330974107201, 19880486910270, 298538277761251, 17932177152585330, 269281195566541201, 16174803911145057390, 242891339862742402051, 14589655195675689180450, 219087719274998080108801

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, 902, 0, -1).

Formula

G.f.: -(x^3-30*x^2-451*x-30) / ((x^2-30*x-1)*(x^2+30*x-1)). - Colin Barker, Nov 09 2013

a(n) = 902*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013

Mathematica

Numerator[Convergents[Sqrt[904], 30]] (* Vincenzo Librandi, Sep 25 2013 *)
CoefficientList[Series[(30 + 451 x + 30 x^2 - x^3)/(1 - 902 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 902, 0, -1}, {30, 451, 27090, 406801}, 20] (* Harvey P. Dale, Sep 04 2023 *)

Prog

(Magma) I:=[30, 451, 27090, 406801]; [n le 4 select I[n] else 902*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013

Crossrefs

Cf. A042747.

Sequence in context: A006421 A035710 A341559 * A281700 A024524 A081736

Adjacent sequences: A042743 A042744 A042745 * A042747 A042748 A042749

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Nov 09 2013

Status

approved