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A214581
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Triangle read by rows: T(n,k) is the number of unordered pairs of nodes at distance k in the circumcoronene H(n) (n=1,2,3,4,5; see definition in the Klavzar papers).
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1
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6, 6, 3, 30, 48, 57, 54, 45, 30, 12, 72, 126, 165, 186, 195, 186, 168, 138, 102, 66, 27, 132, 240, 327, 390, 435, 456, 462, 444, 414, 366, 309, 246, 177, 114, 48, 210, 390, 543, 666, 765, 834, 882, 900, 900, 870, 825, 756, 675, 582, 480, 378, 270, 174, 75
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OFFSET
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1,1
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COMMENTS
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The entries in row n are the coefficients of the Wiener polynomial of the corresponding graph.
Row n contains 4n-1 entries.
T(n,3) = 3(9n^2-9n+1)= 3*A069131(n) (for n>5 this is a conjecture).
T(n,2n) = n(7n^2-1) = 6*A004126(n) (for n>5 this is a conjecture).
T(n,4n-2) = 6(n^2+n-1) = 6*A028387(n-1) (for n>5 this is a conjecture).
T(n,4n-1) = 3n^2 = A033428(n) (for n>5 this is a conjecture).
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LINKS
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FORMULA
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The entries have been obtained by using the Maple Graph Theory package for finding the distance matrix of each of the five graphs H(n) (n=1,2,3,4,5). The given Maple program yields the Wiener polynomial of H(2) (having as coefficients the entries in row 2).
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CROSSREFS
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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