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A143943
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The Wiener index of a chain of n squares joined at vertices (i.e., joined like <><><>...<>; here <> is a square!).
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2
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8, 40, 114, 248, 460, 768, 1190, 1744, 2448, 3320, 4378, 5640, 7124, 8848, 10830, 13088, 15640, 18504, 21698, 25240, 29148, 33440, 38134, 43248, 48800, 54808, 61290, 68264, 75748, 83760, 92318, 101440, 111144, 121448, 132370, 143928
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OFFSET
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1,1
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COMMENTS
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The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
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LINKS
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FORMULA
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a(n) = n*(2 + 3*n + 3*n^2).
G.f.: 2*z*(2 + z)^2/(1 - z)^4.
a(n) = Sum_{k=1..2*n} k*A143942(n,k).
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EXAMPLE
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a(1)=8 because in the graph <> with vertices a,b,c,d we have 4 distances equal to 1 (the edges) and 2 distances equal to 2 (ac and bd); 4*1 + 2*2 = 8.
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MAPLE
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seq(n*(2+3*n+3*n^2), n=1..40);
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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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