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A192835
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Molecular topological indices of the odd graphs.
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2
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0, 24, 540, 12040, 258300, 5258484, 102834732, 1948929840, 36099037260, 656717973340, 11782163004612, 208991112900024, 3673025551895700, 64051241252342400, 1109647124772841800, 19114937411113617120, 327669959548309223340, 5592728044559732561100
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OFFSET
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1,2
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COMMENTS
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The n-odd graph is a vertex transitive graph. The number of nodes at distance k from a specified node for k in 1..n-1 is given by A088459(n,k). Ignore the second half of each row (k>=n). - Andrew Howroyd, May 11 2017
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LINKS
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Eric Weisstein's World of Mathematics, Odd Graph
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FORMULA
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MATHEMATICA
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b[n_] := Sum[Binomial[n-1, i]*Binomial[n, i]*Min[2*i, 2*(n-i)-1], {i, 1, n - 1}];
a[1] = 0; a[n_] := Binomial[2*n - 1, n]*n*(n + b[n]);
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PROG
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(PARI)
b(n)=sum(i=1, n-1, binomial(n-1, i)*binomial(n, i)*min(2*i, 2*(n-i)-1));
a(n)=if(n<2, 0, binomial(2*n-1, n)*n*(n+b(n))); \\ Andrew Howroyd, May 11 2017
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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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