OFFSET
2,2
COMMENTS
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.
FORMULA
T(2n+1,k) = 2n+1 (1<=k<=n); T(2n,k)=2n (1<=k<=n-1); T(2n,n)=n.
G.f. = G(q,z) = qz^2/(1+z-z^2-qz^3)/((1-qz^2)^2*(1-z)^2).
EXAMPLE
T(4,2)=2 because in C_4 (a square) there are 2 distances equal to 2.
Triangle starts:
1;
3;
4, 2;
5, 5;
6, 6, 3;
7, 7, 7;
MAPLE
P:=proc(n) if `mod`(n, 2)=0 then n*(sum(q^j, j=1..(1/2)*n-1))+(1/2)*n*q^((1/2)*n) else n*(sum(q^j, j=1..(1/2)*n-1/2)) end if end proc: for n from 2 to 18 do p[n]:=P(n) end do: for n from 2 to 18 do seq(coeff(p[n], q, j), j=1..floor((1/2)*n)) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 06 2008
STATUS
approved