login
A041677
Denominators of continued fraction convergents to sqrt(357).
2
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
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
Sequence in context: A240120 A177179 A335782 * A153316 A041160 A248305
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 21 2013
STATUS
approved