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Search: id:A143945
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| A143945 |
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The Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices in the graph. |
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2
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| 8, 72, 320, 1000, 2520, 5488, 10752, 19440, 33000, 53240, 82368, 123032, 178360, 252000, 348160, 471648, 627912, 823080, 1064000, 1358280, 1714328, 2141392, 2649600, 3250000, 3954600, 4776408, 5729472, 6828920, 8091000, 9533120
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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a(n)=Sum(k*A143944(n,k),k=1..2n-2).
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REFERENCES
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Y.-N. Yeh and I. Gutman, On the sum of all distances in composite graphs, Discrete Math., 135 (1994), 359-365.
D. Stevanovic, Hosoya polynomial of composite graphs, Discrete Math., 235 (2001), 237-244.
B.-Y. Yang and Y.-N. Yeh, Wiener polynomials of some chemically interesting graphs, International Journal of Quantum Chemistry, 99 (2004), 80-91.
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FORMULA
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a(n)=n^3*(n^2-1)/3.
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EXAMPLE
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a(2)=8 because in P_2 x P_2 (a square) there are 4 distances equal to 1 and 2 distances equal to 2 (4*1 + 2*2 = 8).
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MAPLE
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seq((1/3)*n^3*(n^2-1), n=2..33);
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CROSSREFS
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A143944
Sequence in context: A064015 A044576 A104453 this_sequence A082141 A054615 A111919
Adjacent sequences: A143942 A143943 A143944 this_sequence A143946 A143947 A143948
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 20 2008
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