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Search: id:A094659
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| A094659 |
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Number of closed walks of length n at a vertex of the cyclic graph on 7 nodes C_7. |
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+0
1
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| 1, 0, 2, 0, 6, 0, 20, 2, 70, 18, 252, 110, 924, 572, 3434, 2730, 12902, 12376, 48926, 54264, 187036, 232562, 720062, 980674, 2789164, 4086550, 10861060, 16878420, 42484682, 69242082, 166823430, 282580872, 657178982, 1148548016, 2595874468
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In general a(n,m)=2^n/m*Sum_{k=0..m-1} Cos(2Pi*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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FORMULA
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a(n)=2^n/7*Sum_{k=0..6} Cos(2Pi*k/7)^n); a(n)=7(a(n-2)-2a(n-4)+a(n-6))+2a(n-7); G.f.: (1-x-2x^2+x^3)/((2x-1)(-1-x+2x^2+x^3))
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MATHEMATICA
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f[n_] := FullSimplify[ TrigToExp[ 2^n/7 Sum[Cos[2Pi*k/7]^n, {k, 0, 6}]]]; Table[ f[n], {n, 0, 36}] (from Robert G. Wilson v Jun 09 2004)
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CROSSREFS
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Sequence in context: A081153 A126869 A094233 this_sequence A137437 A021489 A092158
Adjacent sequences: A094656 A094657 A094658 this_sequence A094660 A094661 A094662
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KEYWORD
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nonn
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AUTHOR
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Herbert Kociemba (kociemba(AT)t-online.de), Jun 06 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 09 2004
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