login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052964 Expansion of (1-x)/((1-2x)(1+x-x^2)). 7
1, 0, 3, 1, 10, 7, 35, 36, 127, 165, 474, 715, 1807, 3004, 6995, 12393, 27370, 50559, 107883, 204820, 427351, 826045, 1698458, 3321891, 6765175, 13333932, 26985675, 53457121, 107746282, 214146295, 430470899, 857417220, 1720537327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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, 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, 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, Oct 01 2004

LINKS

Table of n, a(n) for n=0..32.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1035

Index entries for linear recurrences with constant coefficients, signature (1,3,-2).

FORMULA

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)=0}

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, 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, Oct 01 2004

a(n) = (2^(n+1) + Lucas(n+2)*(-1)^n)/5 - Ross La Haye, May 31 2006

MAPLE

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

CROSSREFS

Sequence in context: A046658 A124574 A295856 * A084178 A262030 A260178

Adjacent sequences:  A052961 A052962 A052963 * A052965 A052966 A052967

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 17:55 EDT 2018. Contains 316376 sequences. (Running on oeis4.)