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A320099
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Number of no-leaf subgraphs of the 5 X n grid.
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2
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1, 50, 5193, 583199, 65485654, 7354266811, 825905301851, 92751581627976, 10416273692997679, 1169777980482365913, 131369486228240893660, 14753177269494392259423, 1656824927874469183283433, 186066281959642930757881316, 20895787297635543757965741097
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OFFSET
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1,2
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COMMENTS
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Also, the number of ways to lay unit-length matchsticks on a 5 X n grid of points in such a way that no end is "orphaned".
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LINKS
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FORMULA
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Conjecture: a(n) = 103*a(n-1) + 1063*a(n-2) - 1873*a(n-3) - 20274*a(n-4) + 44071*a(n-5) - 10365*a(n-6) - 20208*a(n-7) + 5959*a(n-8) + 2300*a(n-9) - 500*a(n-10) for n > 10.
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EXAMPLE
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Three of the a(3) = 5193 subgraphs of the 5 X 3 grid with no leaf vertices are:
+---+---+ + + + + +---+
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+---+---+ +---+---+ + +---+
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+---+---+ + +---+ +---+ +
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+---+---+ +---+ + +---+---+
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+---+---+ + + + + +---+
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CROSSREFS
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A093129 is analogous for 2 X (n+1) grids.
A301976 is analogous for 3 X n grids.
A320097 is analogous for 4 X n grids.
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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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