OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
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.: (105 - 66*z)/(1 - 340*z + z^2).
a(n) = ((105 + 24*sqrt(19))/2)*(170 + 39*sqrt(19))^(n) + ((105 - 24*sqrt(19) )/2)*(170 - 39*sqrt(19))^(n).
MAPLE
u(0):=105:u(1):=35634:for n from 0 to 20 do u(n+2):=340*u(n+1)-u(n):od:seq(u(n), n=0..20); taylor(((105+35634*z-105*z*340)/(1-340*z+z^2)), z=0, 20); for n from 0 to 20 do u(n):=simplify((24*sqrt(19)+105)/2*(170+39*sqrt(19))^(n)+(-24*sqrt(19)+105)/2*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20);
MATHEMATICA
LinearRecurrence[{340, -1}, {105, 35634}, 50] (* G. C. Greubel, Jun 23 2016 *)
PROG
(Magma) I:=[105, 35634]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 25 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Nov 11 2009
STATUS
approved