0,3

Number of walks of length n+1 between two adjacent vertices in the cycle graph C_5. Example: a(2)=3 because in the cycle ABCDE we have three walks of length 3 between A and B: ABAB, ABCB, and AEAB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

In general a(n,m)=2^n/m*Sum(k,0,m-1,Cos(2Pi*k/m)^(n+1)) gives number of walks of length n between two adjacent vertices in the cycle graph C_m. Here we have m=5. - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004

Counts walks of length n at the vertex of degree 3 of the graph with adjacency matrix A=[0,1,1,1;1,0,0,0;1,0,0,0;1,0,0,1]. Binomial transform is (L(n-2)+2*3^n)/5, or A099159. - Paul Barry (pbarry(AT)wit.ie), Oct 01 2004

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1035

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

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

Sum(-1/25*(-1-11*_alpha+6*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-_Z-3*_Z^2+2*_Z^3))

a(n-1)=2^n/5*Sum(k, 0, 4, Cos(2Pi*k/5)^(n+1)), n>=1 - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004

a(n)=((sqrt(5)-1)/2)^n(3/10-sqrt(5)/10)+((-sqrt(5)-1)/2)^n(3/10+sqrt(5)/10)+2^(n+1)/5 - Paul Barry (pbarry(AT)wit.ie), Oct 01 2004

a(n) = (2^(n+1) + Lucas(n+2)*(-1)^n)/5 - Ross La Haye (rlahaye(AT)new.rr.com), May 31 2006

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

Sequence in context: A117207 A046658 A124574 this_sequence A084178 A068438 A064060

Adjacent sequences: A052961 A052962 A052963 this_sequence A052965 A052966 A052967

easy,nonn

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000