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A303505
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Number of odd chordless cycles in the n-triangular (Johnson) graph.
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1
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0, 0, 0, 12, 72, 612, 3552, 34632, 247824, 3047544, 26502624, 396071604, 4055072664, 71316639036, 839706878016, 16982482829136, 225984627860256, 5165674068939696, 76644407669629248, 1953726395279874588, 31974794507569558248, 899186672783502993108, 16089847137602083031328
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OFFSET
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2,4
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COMMENTS
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Equivalently, the number of cycles in the complete graph with odd length greater than three. - Andrew Howroyd, Apr 28 2018
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LINKS
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FORMULA
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a(n) = Sum_{k=2, ceiling(n/2)-1} binomial(n, 2*k+1)*(2*k)!/2. - Andrew Howroyd, Apr 28 2018
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MATHEMATICA
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Array[Sum[Binomial[#, 2 k + 1] (2 k)!/2, {k, 2, Ceiling[#/2] - 1}] &, 23, 2] (* Michael De Vlieger, Apr 28 2018 *)
Table[Sum[Binomial[n, 2 k + 1] (2 k)!/2, {k, 2, Ceiling[n/2] - 1}], {n, 2, 20}] (* Eric W. Weisstein, Apr 29 2018 *)
Join[{0, 0, 0}, Table[12 Binomial[n, 5] HypergeometricPFQ[{1, 5/2, (5 - n)/2, 3 - n/2}, {7/2}, 4], {n, 5, 20}]] (* Eric W. Weisstein, Apr 29 2018 *)
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PROG
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(PARI) a(n)=sum(k=2, n\2, binomial(n, 2*k+1)*(2*k)!/2) \\ Andrew Howroyd, Apr 28 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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