A206484 Numerator of the complexity index B of the path graph on n vertices (n>=2).

2, 5, 4, 116, 466, 895, 2011, 11887, 456586, 4673247, 3737, 4105421072, 84949477486, 25869451, 330137431, 7982039918, 726807741125074, 2180011073659, 144755460533, 772879344134036, 193884856434901466474, 324829874191095862, 70339720614511, 184390793325658393

Offset

2,1

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 denominators are A206485.

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_{j=1..n} 1/(n*(n + 1 - 2*j) + 2*j*(j-1))) - 4/(n*(n-1)).

Example

a(3)=5 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: numer(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. A206485.

Sequence in context: A357240 A307131 A210419 * A061083 A177039 A075102

Adjacent sequences: A206481 A206482 A206483 * A206485 A206486 A206487

Keyword

nonn,frac

Author

Emeric Deutsch, Feb 19 2012

Status

approved