OFFSET
2,1
LINKS
B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.
Eric Weisstein's World of Mathematics, Star Graph.
FORMULA
T(m,n) = (m-1)^2+(1/6)n(n^2-19)+(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(2-t-s)(ts^2-2ts+s^2-2s+2)/[(1-t)^3*(1-s)^4].
The Wiener polynomial of the graph F(m,n) is (m-1)t+(1/2)(m-1)(m-2)t^2+t(t^n-nt+n-1)/(1-t)^2+t[1+t+(m-2)t^2](1-t^n)/(1-t).
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: (m-1)^2+(1/6)*n*(n^2-19)+(1/2)*m*n*(n+5) end proc; for n from 2 to 12 do seq(T(n+1-i, i), i = 1 .. n-1) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Sep 27 2010
STATUS
approved