A042923 Denominators of continued fraction convergents to sqrt(993).

1, 1, 2, 41, 43, 84, 5251, 5335, 10586, 217055, 227641, 444696, 27798793, 28243489, 56042282, 1149089129, 1205131411, 2354220540, 147166804891, 149521025431, 296687830322, 6083277631871, 6379965462193, 12463243094064, 779101037294161, 791564280388225

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, 0, 0, 5294, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^4 - x^3 + 2*x^2 + x + 1)*(x^6 - 42*x^3 - 1) / (x^12 - 5294*x^6 + 1). - Colin Barker, Dec 25 2013

a(n) = 5294*a(n-6) - a(n-12) for n > 11. - Vincenzo Librandi, Feb 01 2014

Mathematica

Denominator[Convergents[Sqrt[993], 30]] (* Vincenzo Librandi, Feb 01 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 5294, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 41, 43, 84, 5251, 5335, 10586, 217055, 227641, 444696}, 30] (* Harvey P. Dale, Oct 24 2020 *)

Prog

(Magma) I:=[1, 1, 2, 41, 43, 84, 5251, 5335, 10586, 217055, 227641, 444696]; [n le 12 select I[n] else 5294*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Feb 01 2014

Crossrefs

Cf. A042922, A040961.

Sequence in context: A107194 A235147 A154767 * A222717 A059698 A107190

Adjacent sequences: A042920 A042921 A042922 * A042924 A042925 A042926

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 25 2013

Status

approved