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A095308 Number of walks of length n between two nodes at distance 3 in the cycle graph C_7. 1
1, 1, 5, 6, 21, 28, 84, 121, 331, 507, 1300, 2093, 5110, 8568, 20129, 34885, 79477, 141494, 314489, 572264, 1246784, 2309385, 4950751, 9303411, 19684692, 37427313, 78354346, 150402700, 312168761, 603861897, 1244620149 (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=7 and k=3.

LINKS

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

FORMULA

a(n)= 2^n/7*Sum(r, 0, 6, Cos(6Pi*r/7)Cos(2Pi*r/7)^n) G.f.: x^3/((-1+2x)(-1-x+2x^2+x^3)) a(n)=a(n-1)+4a(n-2)-3a(n-3)-2a(n-4)

CROSSREFS

Sequence in context: A057520 A060423 A037951 * A132796 A006492 A110344

Adjacent sequences:  A095305 A095306 A095307 * A095309 A095310 A095311

KEYWORD

nonn

AUTHOR

Herbert Kociemba, Jul 03 2004

STATUS

approved

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)