A144720 a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2).

2, 3, 10, 37, 138, 515, 1922, 7173, 26770, 99907, 372858, 1391525, 5193242, 19381443, 72332530, 269948677, 1007462178, 3759900035, 14032137962, 52368651813, 195442469290, 729401225347, 2722162432098, 10159248503045

Offset

0,1

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (4,-1).

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

Adjacent sequences: A144717 A144718 A144719 * A144721 A144722 A144723

Keyword

nonn

Author

Michael Somos, Sep 19 2008

Status

approved