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A094233
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Number of closed walks of length n at a vertex of the cyclic graph on 9 nodes C_9.
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2
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1, 0, 2, 0, 6, 0, 20, 0, 70, 2, 252, 22, 924, 156, 3432, 910, 12870, 4760, 48622, 23256, 184796, 108528, 705894, 490314, 2708204, 2163150, 10430500, 9373652, 40313160, 40060078, 156305070, 169345560, 607812102, 709645552, 2369918628, 2952780320
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OFFSET
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0,3
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COMMENTS
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In general, a(n,m) = 2^n/m*Sum_{k=0..m-1} cos(2*Pi*k/m)^n) counts closed walks of length n at a vertex of the cyclic graph on m nodes C_m.
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LINKS
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FORMULA
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a(n) = 2^n/9*Sum_{k=0..8} cos(2*Pi*k/9)^n.
G.f.: -(x-1)*(x^3+3*x^2-1)/((2*x-1)*(x+1)*(x^3-3*x^2+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
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MATHEMATICA
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f[n_] := FullSimplify[ TrigToExp[ 2^n/9 Sum[ Cos[2Pi*k/9]^n, {k, 0, 8}]]]; Table[ f[n], {n, 0, 40}] (* Robert G. Wilson v, Jun 01 2004 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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