OFFSET
1,2
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, Stacked Book Graph.
FORMULA
T(m,n) = (1/6)n[n^2-(m+1)^2+mn(mn+6m+2n)].
The Wiener polynomial p[n](t) of the graph B(m,n) satisfies the recurrence relation p[n] = p[n-1]+mt+(1/2)m(m-1)t^2+[t+mt+2mt^2+m(m-1)t^3]*sum(t^j,j=0..n-2).
EXAMPLE
T(2,1)=4 because B(2,1) reduces to the path graph P(3) which has 2 pairs of nodes at distance 1 and 1 pair at distance 2.
Square array T(m,n) begins:
1, 8, 25, 56, 105, ...
4, 25, 72, 154, 280, ...
9, 52, 145, 304, 545, ...
16, 89, 244, 506, 900, ...
MAPLE
T := proc (m, n) options operator, arrow: (1/6)*n*(n^2-(m+1)^2+m*n*(m*n+2*n+6*m)) end proc: for n to 10 do seq(T(n+1-j, j), j = 1 .. n) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Sep 28 2010
STATUS
approved