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A095368 Number of walks of length n between two nodes at distance 3 in the cycle graph C_9. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 19:03 EDT 2021. Contains 347617 sequences. (Running on oeis4.)