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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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3
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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, 4749439975, 10103745288
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OFFSET
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2,3
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COMMENTS
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In general 2^n/m*Sum_{r=0..m-1} cos(2*Pi*k*r/m)*cos(2*Pi*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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LINKS
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FORMULA
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a(n) = 2^n/7*Sum_{r=0..6} cos(4*Pi*r/7)*cos(2*Pi*r/7)^n).
a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 2*a(n-4).
G.f.: x^2*(1-x) / ((1-2*x)*(1+x-2*x^2-x^3)).
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MATHEMATICA
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LinearRecurrence[{1, 4, -3, -2}, {1, 0, 4, 1}, 40] (* Harvey P. Dale, Sep 22 2019 *)
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PROG
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(PARI) Vec(x^2*(1-x)/((1-2*x)*(1+x-2*x^2-x^3)) + O(x^40)) \\ Colin Barker, Nov 28 2015
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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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STATUS
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approved
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