A095368 Number of walks of length n between two nodes at distance 3 in the cycle graph C_9.

1, 0, 5, 1, 21, 8, 84, 45, 330, 221, 1287, 1015, 5006, 4488, 19465, 19380, 75753, 82365, 295261, 346104, 1152944, 1442101, 4510830, 5969561, 17682795, 24582663, 69448446, 100804436, 273241161, 411921832, 1076832989

Offset

3,3

Comments

In general 2^n/m*Sum(r,0,m-1,Cos(2Pi*k*r/m)Cos(2Pi*r/m)^n) is the number of walks of length n between two nodes at distance k in the cycle graph C_m. Here we have m=9 and k=3.

Links

Table of n, a(n) for n=3..33.

Formula

a(n)= 2^n/9*Sum(r, 0, 8, Cos(2Pi*r/3)Cos(2Pi*r/9)^n) G.f.: (-1+x)x^3/((1+x)(-1+2x)(1-3x^2+x^3)) a(n)=a(n-1)+5a(n-2)-4a(n-3)-5a(n-4)+2a(n-5)

Crossrefs

Sequence in context: A063476 A126325 A278544 * A029757 A146056 A101625

Adjacent sequences: A095365 A095366 A095367 * A095369 A095370 A095371

Keyword

nonn

Author

Herbert Kociemba, Jul 03 2004

Status

approved