0,3

Scaled Chebyshev U-polynomials evaluated at I*sqrt(3)/2.

A. F. Horadam, Special properties of the sequence w_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=q=3.

Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.

W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs. (39), (41) and (45), rhs, m=3.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n)=(-I*sqrt(3))^n*U(n, I*sqrt(3)/2), g.f.: 1/(1-3*x-3*x^2).

a(n) = sum(3^(n-k)*binomial(n-k, k), k=0..floor(n/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 14 2001

a(n) = [p^(n+1) - q^(n+1)]/(sqrt 21); p = (3 + sqrt 21)/2, q = (3 - sqrt 21)/2. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 02 2003

For n > 0, a(n) = Sum_{k=0..n-1} (2^k)*A063967(n-1,k) - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Jul 23 2006

a(n+1)=Sum_{k, 0<=k<=n}2^k*A063967(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2006

G.f.: x/(1-3x-3x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]

CoefficientList[Series[1/(1-3x-3x^2), {x, 0, 25}], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 22 2007

(Other) sage: [lucas_number1(n, 3, -3) for n in xrange(0, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Equals round(A085480(n)/sqrt(21)).

Sequence in context: A062561 A128593 A085481 this_sequence A114515 A151162 A094547

Adjacent sequences: A030192 A030193 A030194 this_sequence A030196 A030197 A030198

nonn

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

Edited by Ralf Stephan, Aug 02 2004

I simplified the definition. As a result the offsets in some of the formulae may need to shifted by 1. - N. J. A. Sloane (njas(AT)research.att.com), Apr 01, 2006.