OFFSET
1,2
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
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 11 2011
EXTENSIONS
a(8)-a(18) from Andrew Howroyd, May 11 2017
STATUS
approved