The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144720 a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2). 1
2, 3, 10, 37, 138, 515, 1922, 7173, 26770, 99907, 372858, 1391525, 5193242, 19381443, 72332530, 269948677, 1007462178, 3759900035, 14032137962, 52368651813, 195442469290, 729401225347, 2722162432098, 10159248503045 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
Sequence satisfies -11 = f(a(n), a(n+1)) where f(u, v) = u^2 + v^2 - 4*u*v.
G.f.: (2 - 5*x) / (1 - 4*x + x^2). a(n) = (11 + a(n-1)^2) / a(n-2).
MATHEMATICA
LinearRecurrence[{4, -1}, {2, 3}, 30] (* Harvey P. Dale, Aug 29 2015 *)
PROG
(PARI) {a(n) = real( (2 + quadgen(12))^n * ( 2 - 1 / quadgen(12) ))}
(PARI) {a(n) = subst( (4*polchebyshev(n) + polchebyshev(n-1)) / 3, x, 2)}
CROSSREFS
Cf. A144721(n) = a(-n).
Sequence in context: A075890 A296269 A141102 * A164933 A003048 A008980
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 19 2008
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 15:23 EDT 2024. Contains 372738 sequences. (Running on oeis4.)