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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!). 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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| T. Mansour and M. Schork, Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs, J. Math. Chemistry, 47, 2010, 72-98 (see Example 5.6).
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FORMULA
| a(n) = n*(2+3*n+3*n^2).
G.f.: 2*z*(2 + z)^2/(1-z)^4.
a(n) = Sum(k*A143942(n,k), k=1..2*n).
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EXAMPLE
| 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
| seq(n*(2+3*n+3*n^2), n=1..40);
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CROSSREFS
| A143942
Sequence in context: A120931 A069083 A014642 * A135796 A105374 A162668
Adjacent sequences: A143940 A143941 A143942 * A143944 A143945 A143946
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 06 2008
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