A192835 Molecular topological indices of the odd graphs.

0, 24, 540, 12040, 258300, 5258484, 102834732, 1948929840, 36099037260, 656717973340, 11782163004612, 208991112900024, 3673025551895700, 64051241252342400, 1109647124772841800, 19114937411113617120, 327669959548309223340, 5592728044559732561100

Offset: 1

Author

Eric W. Weisstein, Jul 11 2011

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Molecular Topological Index
• Eric Weisstein's World of Mathematics, Odd Graph

Crossrefs

Cf. A088459.

Programs

Mathematica

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]);
Array[a, 18] (* Jean-François Alcover, Oct 02 2017, after Andrew Howroyd *)

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

Formula

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

Extensions

a(8)-a(18) from Andrew Howroyd, May 11 2017