3,1

Row n contains floor((n+1)/2) entries.

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

T(n,1)=3n = number of edges in the corresponding graph.

Sum(k*T(n,k), k>=1) = A180857(n).

N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993.

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, Moebius Ladder.

The generating polynomial for row 2n+1 is n[3t+2t^{(n+1)/2}+4t^2*sum(t^j, j=0..(m-5)/2)] and for row 2n it is n[3t+4t^2*sum(t^j, j=0..(n-4)/2)] (these are also the Wiener polynomials of the corresponding Moebius ladders).

Triangle starts:

9,6;

12,16;

15,20,10;

18,24,24;

21,28,28,14;

24,32,32,32;

s := proc (m) options operator, arrow: sum(t^j, j = 0 .. m-2) end proc: P := proc (m) if `mod`(m, 2) = 0 then sort(expand(simplify(m*(3*t+4*t^2*s((1/2)*m))))) else sort(expand(simplify(m*(3*t+4*t^2*s((1/2)*m-1/2)+2*t^((1/2)*m+1/2))))) end if end proc: for m from 3 to 16 do P(m) end do: for n from 3 to 16 do seq(coeff(P(n), t, i), i = 1 .. floor((n+1)*1/2)) end do; # yields sequence in triangular form

Cf. A000384, A180857.

Sequence in context: A063602 A180572 A182873 * A166520 A102648 A389647

Adjacent sequences: A180853 A180854 A180855 * A180857 A180858 A180859

nonn,tabf

Emeric Deutsch, Sep 24 2010

approved