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%I #9 Mar 30 2012 17:36:29
%S 1,3,3,105,495,1092,2772,18270,774225,8666515,7524,8918270907,
%T 198041889045,64422540,874639920,22416484563,2156747215916961,
%U 6815795571585,475605193700,2662311296532195,698714939635041136731,1222290775374865581,275870385659700,752514157132795200
%N Denominator of the complexity index B of the path graph on n vertices (n>=2).
%C The complexity index B of a graph G is defined as Sum(a[i]/d[i]), where a[i] is the degree of the vertex i and d[i] is the distance degree of i (the sum of distances from i to all the vertices of G), the summation being over all the vertices of G (see the Bonchev & Buck reference, p. 215).
%C The numerators are A206484.
%D D. Bonchev and G. A. Buck, Quantitative measures of network complexity, in: Complexity in Chemistry, Biology, and Ecology, Springer, New York, pp. 191-235.
%F The complexity index B of the path on n vertices is 4*Sum{1/[n(n+1-2j)+2j(j-1)], j=1..n} - 4/[n(n-1)].
%e a(3)=3 because the vertices of the path ABC have degrees 1, 2, 1 and distance degrees 3, 2, 3; then 1/3 + 2/2 + 1/3 = 5/3.
%p a := proc (n) options operator, arrow: denom(4*(sum(1/(n*(n+1-2*j)+2*j*(j-1)), j = 1 .. n))-4/(n*(n-1))) end proc: seq(a(n), n = 2 .. 25);
%Y Cf. A206484.
%K nonn,frac
%O 2,2
%A _Emeric Deutsch_, Feb 19 2012
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