0,2

Number of Hamiltonian cycles in K_3 X P_n.

Number of ternary squarefree words of length n.

Row sums of A029635. - Paul Barry (pbarry(AT)wit.ie), Jan 30 2005

Binomial transform is {1, 4, 13, 40, 121, 364, ...}, see A003462 . -Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005

Convolved with the Jacobsthal sequence A001045 = A001786: (1, 4, 12, 32, 80,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 23 2009]

Equals (n+1)-th row sums of triangle A161175 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 05 2009]

a(n) written in base 2: a(0) = 1, a(n) for n >= 1: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-1) times 0 (see A003953(n)). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 17 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Index entries for sequences related to trees

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 151

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 304

F. Faase, Counting Hamilton cycles in product graphs

C. Richard and U. Grimm, On the entropy and letter frequencies of ternary square-free words

G.f.: (1+x)/(1-2*x)

a(n)=2a(n-1), n>1; a(0)=1, a(1)=3.

Binomial transform of A000034. a(n)=(3*2^n-0^n)/2 - Paul Barry (pbarry(AT)wit.ie), Apr 29 2003

a(n)=sum{k=0..n, (n+k)binomial(n, k)/n} - Paul Barry (pbarry(AT)wit.ie), Jan 30 2005

a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005

Binomial transform of A000034. Hankel transform is {1,-3,0,0,0,...}. - Paul Barry (pbarry(AT)wit.ie), Aug 29 2006

Row sums of triangle A133084 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 08 2007

a(0) = 1, a(n) = 3*2^(n-1) = 2^n + 2^(n-1) for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 17 2009]

k := 3; if n = 0 then 1 else k*(k-1)^(n-1); fi;

with(combinat):a:=n->stirling2(n, 2)-stirling2(n-2, 2): seq(a(n), n=2..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007

with(finance):seq(floor(futurevalue(3, 1, n)), n=-1..27); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 24 2009]

(Other) SAGE:[lucas_number1(n, 2, 0)+lucas_number1(n+1, 2, 0)for n in xrange(0, 29)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]

Essentially same as A007283 (3*2^n) and A042950.

Cf. A133084.

A001787, A001045 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 23 2009]

A161175 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 05 2009]

Adjacent sequences: A003942 A003943 A003944 this_sequence A003946 A003947 A003948

Sequence in context: A115805 A046944 A122391 this_sequence A007283 A049942 A099844

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).