0,4

a(n) is the coefficient of x^(n-1) in the bivariate Fibonacci polynomials F(n)(x,y)=xF(n-1)(x,y)+yF(n-2)(x,y), F(0)(x,y)=0, F(1)(x,y)=1, when y=6x^2. - Mario Catalani (mario.catalani(AT)unito.it), Dec 06 2002

Starting with offset 1 and convolved with (1, 3, 3, 3,...) = A003462: (1, 4, 13, 40,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 28 2009]

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for sequences related to linear recurrences with constant coefficients

Joerg Arndt, Fxtbook

G.f.: x/((1+2*x)*(1-3*x)). a(n)=a(n-1)+6*a(n-2).

a(n)=(1/5)*((3^n)-((-2)^n)) (henryk.wicke(AT)stud.uni-hannover.de)

E.g.f. (exp(3x)-exp(-2x))/5. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2003

a(n+1)=sum(k=0, ceil(n/2), 6^k*binomial(n-k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004

a(n)=(A000244(n)-A001045(n+1)(-1)^n-A001045(n)(-1)^n)/5. - Paul Barry (pbarry(AT)wit.ie), Apr 27 2004

The binomial transform of [1,1,7,13,55,133,463,...] is A122117 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 19 2006

a(n+1)=Sum_{k, 0<=k<=n} A109466(n,k)*(-6)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]

(PARI) a(n)=(3^n-(-2)^n)/5

(Other) sage: [lucas_number1(n, 1, -6) for n in xrange(0, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Cf. A016153.

A003462 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 28 2009]

Sequence in context: A108056 A018562 A112540 this_sequence A091005 A133664 A143794

Adjacent sequences: A015438 A015439 A015440 this_sequence A015442 A015443 A015444

nonn,easy,nice

Olivier Gerard (olivier.gerard(AT)gmail.com)