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A095307
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Number of walks of length n between two nodes at distance 2 in the cycle graph C_7.
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1
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1, 0, 4, 1, 15, 7, 56, 37, 210, 176, 793, 793, 3017, 3458, 11561, 14756, 44592, 62017, 172995, 257775, 674520, 1062601, 2641366, 4352660, 10381281, 17742621, 40927033, 72048354, 161766061, 291693136, 640758252, 1178135905, 2542557383
(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=7 and k=2.
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FORMULA
| a(n)= 2^n/7*Sum(r, 0, 6, Cos(4Pi*r/7)Cos(2Pi*r/7)^n) G.f.: (1-x)x^2/((-1+2x)(-1-x+2x^2+x^3)) a(n)=a(n-1)+4a(n-2)-3a(n-3)-2a(n-4)
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CROSSREFS
| Sequence in context: A107873 A156290 A080419 * A159764 A124029 A056920
Adjacent sequences: A095304 A095305 A095306 * A095308 A095309 A095310
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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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