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A095367
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Number of walks of length n between two nodes at distance 2 in the cycle graph C_9.
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0
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1, 0, 4, 0, 15, 1, 56, 9, 210, 56, 792, 299, 3003, 1470, 11441, 6868, 43776, 31008, 168151, 136629, 648208, 591261, 2507046, 2523676, 9726080, 10656387, 37839375, 44612702, 147600981, 185477216, 577147212, 766744608, 2261792303
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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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=2.
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FORMULA
| a(n)= 2^n/9*Sum(r, 0, 8, Cos(4Pi*r/9)Cos(2Pi*r/9)^n) G.f.: x^2(-1+x+x^2)/((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: A117788 A006710 A081162 * A059065 A170771 A170772
Adjacent sequences: A095364 A095365 A095366 * A095368 A095369 A095370
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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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