3,1

Number of entries in row n = 2 + floor(n/2).

Sum of entries in row n = n(2n-1)=A000384(n).

Sum(k*T(n,k),k>=1) = A180574(n).

B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.

D. Stevanovic, Hosoya polynomial of composite graphs, Discrete Math., 235 (2001), 237-244.

The generating polynomial of row 2n is 2nt-nt^n*(1+t)^2+2nt(1+t)^2*sum(t^j, j=0..n-1); the generating polynomial of row 2n+1 is (2n+1)t[1+(1+t)^2*sum(t^j,j=0..n-1)]; these are the Wiener polynomials of the corresponding graphs.

Triangle starts:

6,6,3;

8,10,8,2;

10,15,15,5;

12,18,21,12,3;

P := proc (n) if `mod`(n, 2) = 0 then sort(expand(n*t*(1+t)^2*(sum(t^j, j = 0 .. (1/2)*n-1))+n*t-(1/2)*n*t^((1/2)*n)*(1+t)^2)) else sort(expand(n*t*(1+(1+t)^2*(sum(t^j, j = 0 .. (1/2)*n-3/2))))) end if end proc; for n from 3 to 15 do P(n) end do: for n from 3 to 15 do seq(coeff(P(n), t, i), i = 1 .. 2+floor((1/2)*n)) end do; # yields sequence in trianguklar form

Cf. A000384, A180574

Sequence in context: A088454 A095228 A021605 * A388696 A143937 A019133

Adjacent sequences: A180570 A180571 A180572 * A180574 A180575 A180576

nonn,tabf

Emeric Deutsch, Sep 19 2010

approved