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A180569
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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.
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4
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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
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Grid Graph.
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FORMULA
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a(n) = (1/2)*n*(n+3)*(3n-1).
G.f.: z*(4+9*z-4*z^2)/(1-z)^4.
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EXAMPLE
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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.
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MAPLE
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seq((1/2)*n*(n+3)*(3*n-1), n = 1 .. 40);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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