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A338527
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Number of spanning trees in the join of the disjoint union of two complete graphs each on n and n+1 vertices with the empty graph on n+1 vertices.
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1
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24, 13500, 34420736, 239148450000, 3520397039081472, 94458953432730437824, 4179422085120000000000000, 283894102615246085842939590912, 28059580711858187192007680000000000, 3870669526565955444680027453177986243584
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OFFSET
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1,1
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COMMENTS
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Equivalently, the graph can be described as the graph on 3*n + 2 vertices with labels 0..3*n+1 and with i and j adjacent iff i+j> 0 mod 3.
These graphs are cographs.
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LINKS
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FORMULA
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a(n) = (n + 1)*(2 n + 2)^n*(2 n + 1)^(2 n - 1).
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EXAMPLE
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The adjacency matrix of the graph associated with n = 2 is: (compare A204437)
[0, 1, 0, 0, 0, 1, 1, 1]
[1, 0, 0, 0, 0, 1, 1, 1]
[0, 0, 0, 1, 1, 1, 1, 1]
[0, 0, 1, 0, 1, 1, 1, 1]
[0, 0, 1, 1, 0, 1, 1, 1]
[1, 1, 1, 1, 1, 0, 0, 0]
[1, 1, 1, 1, 1, 0, 0, 0]
[1, 1, 1, 1, 1, 0, 0, 0]
a(2) = 13500 because the graph has 13500 spanning trees.
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MATHEMATICA
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Table[(n + 1)*(2 n + 2)^n*(2 n + 1)^(2 n - 1), {n, 1, 10}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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