OFFSET
2,1
COMMENTS
REFERENCES
I. Gutman, SL Lee, CH Chu. YLLuo, Indian J. Chem., 33A, 603.
I. Gutman, W. Linert, I. Lukovits, and Z. Tomovic, On the multiplicative Wiener index and its possible chemical applications, Monatshefte fur Chemie, 131, 421-427 (see Eq. between (10) and (11); replace n with n+2).
FORMULA
The generating polynomial of row n is t*(9t^(n+2) - 3nt^3 - 8t^2 - 2t + 1 + 3n)/(1-t)^2.
The bivariate g.f. is G = tz^2*(7 + 12t + 9t^2 - 4z - 13tz + 4tz^2 + 6t^2*z^2 - 12t^2*z)/((1-z)^2*(1-tz)).
EXAMPLE
T(2,3)=9 because in the graph \|/_\|/ there are 9 unordered pairs of vertices at distance 3.
Triangle starts:
7, 12, 9;
10, 18, 18, 9;
13, 24, 27, 18, 9;
16, 30, 36, 27, 18, 9;
MAPLE
for n from 2 to 11 do P[n] := sort(expand(simplify(t*(9*t^(n+2)-3*n*t^3-8*t^2-2*t+1+3*n)/(1-t)^2))) end do: for n from 2 to 11 do seq(coeff(P[n], t, j), j = 1 .. n+1) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 16 2010
STATUS
approved