0,2

Coordination sequence for infinite tree with valency 3.

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]

F. Faase, Counting Hamilton cycles in product graphs

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 151

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 304

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

Index entries for sequences related to linear recurrences with constant coefficients

Index entries for sequences related to trees

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

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

More generally, the g.f. (1+x)/(1-kx) produces the sequence [1, 1 + k, (1 + k)*k, (1 + k)*k^2,... (1+k)*k^(n-1),...], with a(0) = 1, a(n) = (1+k)*k^(n-1) for n >= 1. Also a(n+1) = k*a(n) for n >= 1. - Zak Seidov and njas, Dec 05 2009

The g.f. (1+x)/(1-kx) produces the sequence with closed form (in PARI notation) a(n)=(n>=0)*k^n+(n>=1)*k^(n-1). - Jaume Oliver i Lafont, Dec 05 2009

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, A161175.

Generating functions of the form (1+x)/(1-kx) for k=1 to 12: A040000, A003945, A003946, A003947, A003948, A003949, A003950, A003951, A003952

Generating functions of the form (1+x)/(1-kx) for k=13 to 30: A170732 A170733 A170734 A170735 A170736 A170737 A170738 A170739 A170740 A170741 A170742 A170743 A170744 A170745 A170746 A170747 A170748

Generating functions of the form (1+x)/(1-kx) for k=31 to 50: A170749 A170750 A170751 A170752 A170753 A170754 A170755 A170756 A170757 A170758 A170759 A170760 A170761 A170762 A170763 A170764 A170765 A170766 A170767 A170768 A170769

Sequence in context: A115805 A046944 A122391 this_sequence A007283 A049942 A099844

Adjacent sequences: A003942 A003943 A003944 this_sequence A003946 A003947 A003948

nonn,easy,new

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

Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.