OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (340, -1).
FORMULA
a(n+2) = 340*a(n+1) - a(n).
a(n+1) = 170*a(n) + 39*sqrt(19*a(n)^2 - 1539).
G.f.: (959 - 10*z)/(1 - 340*z + z^2).
a(n) = (220*sqrt(19) + 959)/2*(170 + 39*sqrt(19))^n + (-220*sqrt(19) + 959)/2*(170 - 39*sqrt(19))^n. - Richard Choulet, Nov 13 2009
a(n) = 10*cosh(x*log(170 + 39*Sqrt[19])) - Sqrt[19]*sinh(x*log(170 + 39*Sqrt[19])). - Harvey P. Dale, Aug 06 2013
MAPLE
u(0):=959:u(1):=326050:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n), n=0..20); taylor(((959+326050*z-959*z*340)/(1-340*z+z^2)), z=0, 20); for n from 0 to 20 do u(n):=simplify((220*sqrt(19)+959)/2*(170+39*sqrt(19))^(n)+(-220*sqrt(19)+959)/2*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20);
MATHEMATICA
LinearRecurrence[{340, -1}, {959, 326050}, 20] (* Harvey P. Dale, Aug 06 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Nov 11 2009
STATUS
approved