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A180862 Square array read by antidiagonals: T(m,n) is the Wiener index of the flower graph F(m,n) (m>=2, n>=1). F(m,n) is the graph obtained by joining with an edge a node in the star graph on m nodes to an end-node of the path graph P_n. The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. 0
4, 10, 10, 18, 20, 20, 28, 32, 35, 35, 40, 46, 52, 56, 56, 54, 62, 71, 79, 84, 84, 70, 80, 92, 104, 114, 120, 120, 88, 100, 115, 131, 146, 158, 165, 165, 108, 122, 140, 160, 180, 198, 212, 220, 220, 130, 146, 167, 191, 216, 240, 261, 277, 286, 286, 154, 172, 196, 224 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..60.

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, Star Graph.

FORMULA

T(m,n) = (m-1)^2+(1/6)n(n^2-19)+(1/2)mn(n+5).

G.f.: G(t,s)=Sum(Sum(T(m,n)*t^m*s^n, n=1..infinity),m=2..infinity) = t^2*s(2-t-s)(ts^2-2ts+s^2-2s+2)/[(1-t)^3*(1-s)^4].

The Wiener polynomial of the graph F(m,n) is (m-1)t+(1/2)(m-1)(m-2)t^2+t(t^n-nt+n-1)/(1-t)^2+t[1+t+(m-2)t^2](1-t^n)/(1-t).

EXAMPLE

Square array T(i,j) begins:

4, 10, 20, 35, 56, 84, ...

10, 20, 35, 56, 84, 120, ...

18, 32, 52, 79, 114, 158, ...

28, 46, 71, 104, 146, 198, ...

MAPLE

T := proc (m, n) options operator, arrow: (m-1)^2+(1/6)*n*(n^2-19)+(1/2)*m*n*(n+5) end proc; for n from 2 to 12 do seq(T(n+1-i, i), i = 1 .. n-1) end do; # yields sequence in triangular form

CROSSREFS

Sequence in context: A111072 A189895 A310333 * A310334 A310335 A352753

Adjacent sequences:  A180859 A180860 A180861 * A180863 A180864 A180865

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Sep 27 2010

STATUS

approved

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)