

A180862


Square array read by antidiagonals: T(m,n) is the Wiener index of the flower graph F(m,n) (m>=2, n>=1). F(m,n) is the graph obtained by joining with an edge a node in the star graph on m nodes to an endnode of the path graph P_n. The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.


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4, 10, 10, 18, 20, 20, 28, 32, 35, 35, 40, 46, 52, 56, 56, 54, 62, 71, 79, 84, 84, 70, 80, 92, 104, 114, 120, 120, 88, 100, 115, 131, 146, 158, 165, 165, 108, 122, 140, 160, 180, 198, 212, 220, 220, 130, 146, 167, 191, 216, 240, 261, 277, 286, 286, 154, 172, 196, 224
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OFFSET

2,1


LINKS

Table of n, a(n) for n=2..60.
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, Star Graph.


FORMULA

T(m,n) = (m1)^2+(1/6)n(n^219)+(1/2)mn(n+5).
G.f.: G(t,s)=Sum(Sum(T(m,n)*t^m*s^n, n=1..infinity),m=2..infinity) = t^2*s(2ts)(ts^22ts+s^22s+2)/[(1t)^3*(1s)^4].
The Wiener polynomial of the graph F(m,n) is (m1)t+(1/2)(m1)(m2)t^2+t(t^nnt+n1)/(1t)^2+t[1+t+(m2)t^2](1t^n)/(1t).


EXAMPLE

Square array T(i,j) begins:
4, 10, 20, 35, 56, 84, ...
10, 20, 35, 56, 84, 120, ...
18, 32, 52, 79, 114, 158, ...
28, 46, 71, 104, 146, 198, ...


MAPLE

T := proc (m, n) options operator, arrow: (m1)^2+(1/6)*n*(n^219)+(1/2)*m*n*(n+5) end proc; for n from 2 to 12 do seq(T(n+1i, i), i = 1 .. n1) end do; # yields sequence in triangular form


CROSSREFS

Sequence in context: A111072 A189895 A310333 * A310334 A310335 A352753
Adjacent sequences: A180859 A180860 A180861 * A180863 A180864 A180865


KEYWORD

nonn,tabl


AUTHOR

Emeric Deutsch, Sep 27 2010


STATUS

approved



