A041677 Denominators of continued fraction convergents to sqrt(357).

1, 1, 9, 19, 161, 180, 6641, 6821, 61209, 129239, 1095121, 1224360, 45172081, 46396441, 416343609, 879083659, 7449012881, 8328096540, 307260488321, 315588584861, 2831969167209, 5979526919279, 50668184521441, 56647711440720, 2089985796387361, 2146633507828081

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, 6802, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 -x^9 +9*x^8 -19*x^7 +161*x^6 -180*x^5 -161*x^4 -19*x^3 -9*x^2 -x -1) / ((x^4 -19*x^2 +1)*(x^8 +19*x^6 +360*x^4 +19*x^2 +1)). - Colin Barker, Nov 21 2013

a(n) = 6802*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[357], 30]] (* Harvey P. Dale, Nov 04 2011 *)
CoefficientList[Series[-(x^10 - x^9 + 9 x^8 - 19 x^7 + 161 x^6 - 180 x^5 - 161 x^4 - 19 x^3 - 9 x^2 - x - 1)/((x^4 - 19 x^2 + 1) (x^8 + 19 x^6 + 360 x^4 + 19 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 9, 19, 161, 180, 6641, 6821, 61209, 129239, 1095121, 1224360]; [n le 12 select I[n] else 6802*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041676, A040338.

Sequence in context: A240120 A177179 A335782 * A153316 A041160 A248305

Adjacent sequences: A041674 A041675 A041676 * A041678 A041679 A041680

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved