OFFSET
0,3
COMMENTS
This is the Lucas U(P=3, Q=5) sequence. - R. J. Mathar, Oct 24 2012
a(n+2)/a(n+1) equals the continued fraction 3 - 5/(3 - 5/(3 - 5/(3 - ... - 5/3))) with n 5's. - Greg Dresden, Oct 06 2019
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Wikipedia, Lucas sequence
Index entries for linear recurrences with constant coefficients, signature (3,-5).
FORMULA
G.f.: x/(1 - 3*x + 5*x^2). - Philippe Deléham, Oct 11 2011
E.g.f.: 2*exp(3*x/2)*sin(sqrt(11)*x/2)/sqrt(11). - Stefano Spezia, Oct 06 2019
MATHEMATICA
LinearRecurrence[{3, -5}, {0, 1}, 50]
PROG
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3x+5*x^2))) \\ G. C. Greubel, Jan 25 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 5*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, May 24 2011
STATUS
approved