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A180569 The Wiener index of the P_3 x P_n grid, where P_m is the path graph on m nodes. The Wiener index of a connected graph is the sum of distances between all unordered pairs of nodes in the graph. 4
4, 25, 72, 154, 280, 459, 700, 1012, 1404, 1885, 2464, 3150, 3952, 4879, 5940, 7144, 8500, 10017, 11704, 13570, 15624, 17875, 20332, 23004, 25900, 29029, 32400, 36022, 39904, 44055, 48484, 53200, 58212, 63529, 69160, 75114, 81400, 88027, 95004 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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, Grid Graph.

FORMULA

a(n) = (1/2)*n*(n+3)*(3n-1).

G.f.: z*(4+9z-4z^2)/(1-z)^4.

a(n) = Sum_{k=1..n+1} k*A180568(n,k). - corrected by Andrew Howroyd, May 27 2017

EXAMPLE

a(1)=4 because in P_3 x P_1 = P_3 there are 2 pairs of nodes at distance 1 and one pair at distance 2.

MAPLE

seq((1/2)*n*(n+3)*(3*n-1), n = 1 .. 40);

MATHEMATICA

Table[n (n + 3) (3 n - 1)/2, {n, 39}] (* or *)

Rest@ CoefficientList[Series[x (4 + 9 x - 4 x^2)/(1 - x)^4, {x, 0, 39}], x] (* Michael De Vlieger, May 28 2017 *)

CROSSREFS

Row 3 of A143368.

Cf. A180568.

Sequence in context: A281339 A298282 A077205 * A302821 A125309 A273361

Adjacent sequences:  A180566 A180567 A180568 * A180570 A180571 A180572

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Sep 28 2010

STATUS

approved

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Last modified April 22 14:13 EDT 2019. Contains 322349 sequences. (Running on oeis4.)