0,3

Form the graph with matrix A=[0,1,1;1,0,0;1,0,1] (P_3 with a loop at an extremity). Then A052547 counts closed walks of length n at the degree 2 vertex. - Paul Barry (pbarry(AT)wit.ie), Oct 02 2004

The characteristic polynomial x^3 - x^2 - 2*x + 1 generates a 3 step recursion: a(0)=1,a(1)=0,a(2)=2, for n>2 a(n)=a(n-1)+2*a(n-2)-a(n-3) so we can also prepend the term 1,0 to a(n) and get the same sequence, i.e. start with a(0)=1,a(1)=0,a(2)=1. - Lambert Klasen (lambert.klasen(AT)gmx.net), Jan 30 2005

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 483

a(n)=5a(n-2)-6a(n-4)+a(n-6). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 02 2005

G.f.: -(-1+x)/(x^3-2*x^2-x+1)

Recurrence: {a(1)=0, a(0)=1, a(2)=2, a(n)-2*a(n+1)-a(n+2)+a(n+3)}

Sum(-1/7*_alpha*(-3+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^3-2*_Z^2-_Z+1))

spec := [S, {S=Sequence(Prod(Z, Union(Z, Prod(Z, Sequence(Z)))))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

(PARI) a(n)=if(n==0, 1, if(n==1, 0, if(n==2, 1, a(n-1)+2*a(n-2)-a(n-3)))) for(i=0, 20, print1(a(i), ", ")) (Klasen)

Cf. A096976, A028495.

Sequence in context: A124226 A032006 A074392 this_sequence A096976 A119245 A128731

Adjacent sequences: A052544 A052545 A052546 this_sequence A052548 A052549 A052550

easy,nonn

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000