OFFSET
1,2
COMMENTS
The Wiener polynomial of the graph L(m,n) is (1/2)m(m-1)t + t[t^{n+1}-(n+1)t+n]/(1-t)^2 + (m-1)t^2(1-t^n)/(1-t).
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, Lollipop Graph.
FORMULA
T(m,n) = (1/6)n(n^2-7)+(1/2)m(m+n^2+3n-1).
EXAMPLE
Square array T(i,j) begins:
1 4 10 20 35 56 84 ...
4 10 20 35 56 84 120 ...
8 17 31 51 78 113 157 ...
13 25 43 68 101 143 195 ...
MAPLE
T := proc (m, n) options operator, arrow: (1/6)*n*(n^2-7)+(1/2)*m*(m+n^2+3*n-1) end proc: for m to 11 do seq(T(m+1-j, j), j = 1 .. m) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Sep 22 2010
STATUS
approved