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A095369
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Number of walks of length n between two nodes at distance 4 in the cycle graph C_9.
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0
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1, 1, 6, 7, 28, 36, 120, 165, 495, 716, 2003, 3018, 8024, 12512, 31977, 51357, 127110, 209475, 504736, 850840, 2003784, 3445885, 7956715, 13926276, 31609071, 56191734, 125640180, 226444616, 499685777, 911607609, 1988440598
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,3
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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=4.
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FORMULA
| a(n)= 2^n/9*Sum(r, 0, 8, Cos(8Pi*r/9)Cos(2Pi*r/9)^n). G.f.: x^4/((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)
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CROSSREFS
| Sequence in context: A129214 A042419 A037956 * A006493 A037375 A159582
Adjacent sequences: A095366 A095367 A095368 * A095370 A095371 A095372
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KEYWORD
| nonn
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AUTHOR
| Herbert Kociemba (kociemba(AT)t-online.de), Jul 03 2004
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