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A192835 Molecular topological indices of the odd graphs.

%I A192835 #21 Feb 16 2025 08:33:15
%S A192835 0,24,540,12040,258300,5258484,102834732,1948929840,36099037260,
%T A192835 656717973340,11782163004612,208991112900024,3673025551895700,
%U A192835 64051241252342400,1109647124772841800,19114937411113617120,327669959548309223340,5592728044559732561100
%N A192835 Molecular topological indices of the odd graphs.
%C A192835 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
%H A192835 Andrew Howroyd, <a href="/A192835/b192835.txt">Table of n, a(n) for n = 1..100</a>
%H A192835 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%H A192835 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddGraph.html">Odd Graph</a>
%F A192835 a(n) = binomial(2*n-1, n)*n * (n + Sum_{k=1..n-1} k*A088459(n,k)) for n>1. - _Andrew Howroyd_, May 11 2017
%t A192835 b[n_] := Sum[Binomial[n-1, i]*Binomial[n, i]*Min[2*i, 2*(n-i)-1], {i, 1, n - 1}];
%t A192835 a[1] = 0; a[n_] := Binomial[2*n - 1, n]*n*(n + b[n]);
%t A192835 Array[a, 18] (* _Jean-François Alcover_, Oct 02 2017, after _Andrew Howroyd_ *)
%o A192835 (PARI)
%o A192835 b(n)=sum(i=1,n-1,binomial(n-1,i)*binomial(n,i)*min(2*i,2*(n-i)-1));
%o A192835 a(n)=if(n<2,0,binomial(2*n-1,n)*n*(n+b(n))); \\ _Andrew Howroyd_, May 11 2017
%Y A192835 Cf. A088459.
%K A192835 nonn
%O A192835 1,2
%A A192835 _Eric W. Weisstein_, Jul 11 2011
%E A192835 a(8)-a(18) from _Andrew Howroyd_, May 11 2017