

A180859


Square array read by antidiagonals: T(m,n) is the Wiener index of the windmill graph D(m,n) obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs; m>=2, n>=1).


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1, 3, 4, 6, 14, 9, 10, 30, 33, 16, 15, 52, 72, 60, 25, 21, 80, 126, 132, 95, 36, 28, 114, 195, 232, 210, 138, 49, 36, 154, 279, 360, 370, 306, 189, 64, 45, 200, 378, 516, 575, 540, 420, 248, 81, 55, 252, 492, 700, 825, 840, 742, 552, 315, 100, 66, 310, 621, 912, 1120
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OFFSET

2,2


COMMENTS

The Wiener index of a connected graph is the sum of the distances between all unordered pairs of nodes in the graph.
For the Wiener indices of D(3,n), D(4,n), D(5,n) and D(6,n) see A033991, A152743, A028994, and A180577, respectively.


LINKS

Table of n, a(n) for n=2..61.
B. E. Sagan, YN. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959969.
Eric Weisstein's World of Mathematics, Windmill Graph.


FORMULA

T(m,n) = (1/2)n(m1)((m1)(2n1)+1).
The Wiener polynomial of D(m,n) is (1/2)n(m1)t((m1)(n1)t+m).


EXAMPLE

T(3,2)=14 because the graph D(3,2) consists of two triangles OAB and OCD with a common node O; it has 6 distances equal to 1 (the edges) and 4 distances equal to 2 (AC, AD, BC, and BD); 6 * 1 + 4 * 2 = 14.
Square array starts:
1, 4, 9, 16, 25, ...
3, 14, 33, 60, 95, ...
6, 30, 72, 132, 210, ...
10, 52, 126, 232, 370, ...


MAPLE

T := proc (m, n) options operator, arrow: (1/2)*n*(m1)*((m1)*(2*n1)+1) end proc: for p from 2 to 12 do seq(T(p+1j, j), j = 1 .. p1) end do; # yields sequence in triangular form


CROSSREFS

Cf. A028994, A033991, A152743, A180577.
Sequence in context: A318345 A143100 A327584 * A271618 A137820 A049892
Adjacent sequences: A180856 A180857 A180858 * A180860 A180861 A180862


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Sep 25 2010


STATUS

approved



