A206485 Denominator of the complexity index B of the path graph on n vertices (n>=2).

1, 3, 3, 105, 495, 1092, 2772, 18270, 774225, 8666515, 7524, 8918270907, 198041889045, 64422540, 874639920, 22416484563, 2156747215916961, 6815795571585, 475605193700, 2662311296532195, 698714939635041136731, 1222290775374865581, 275870385659700, 752514157132795200

Offset

2,2

Comments

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).

The numerators are A206484.

References

D. Bonchev and G. A. Buck, Quantitative measures of network complexity, in: Complexity in Chemistry, Biology, and Ecology, Springer, New York, pp. 191-235.

Links

Table of n, a(n) for n=2..25.

Formula

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)].

Example

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.

Maple

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);

Crossrefs

Cf. A206484.

Sequence in context: A010266 A215560 A325486 * A009491 A176614 A173797

Adjacent sequences: A206482 A206483 A206484 * A206486 A206487 A206488

Keyword

nonn,frac

Author

Emeric Deutsch, Feb 19 2012

Status

approved