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Search: id:A095932
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| A095932 |
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Number of walks of length 2n+1 between two nodes at distance 3 in the cycle graph C_10. |
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+0
1
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| 1, 5, 22, 93, 385, 1574, 6385, 25773, 103702, 416405, 1669801, 6690150, 26789257, 107232053, 429124630, 1717012749, 6869397265, 27481113638, 109933682017, 439758885885, 1759098789526, 7036560738245, 28146676447417
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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=10 and k=3.
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FORMULA
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a(n)= 4^n/5*Sum_{r=0..9} Cos(3Pi*r/5)Cos(Pi*r/5)^(2n+1); a(n)=7a(n-1)-13a(n-2)+4a(n-3); G.f.: (-x+2x^2)/((-1+4x)(1-3x+x^2))
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MATHEMATICA
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f[n_]:=FullSimplify[TrigToExp[(4^n/5)Sum[Cos[3Pi*k/5]Cos[Pi*k/5]^(2n+1), {k, 0, 9}]]]; Table[f[n], {n, 1, 35}]
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CROSSREFS
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Adjacent sequences: A095929 A095930 A095931 this_sequence A095933 A095934 A095935
Sequence in context: A071715 A010036 A127617 this_sequence A000346 A026672 A049652
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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), Jul 12 2004
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