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A320097
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Number of no-leaf subgraphs of the 4 X n grid.
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3
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1, 15, 463, 16372, 583199, 20788249, 741026781, 26415034787, 941604528692, 33564941612743, 1196473967526971, 42650154782713601, 1520330364358307239, 54194514148101568538, 1931846809485041315873, 68863650758427752078777, 2454750745501814744040599
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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 4 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) = 36*a(n-1) - 7*a(n-2) - 201*a(n-3) + 49*a(n-4) + 20*a(n-5) - 5*a(n-6) for all n > 6.
Empirical g.f.: x*(1 - 21*x - 70*x^2 + 10*x^3 + 14*x^4 - 3*x^5) / (1 - 36*x + 7*x^2 + 201*x^3 - 49*x^4 - 20*x^5 + 5*x^6). - Colin Barker, Oct 20 2018
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EXAMPLE
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Three of the a(3) = 463 subgraphs of the 4 X 3 grid with no leaf vertices are
+ +---+ + + + + +---+
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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.
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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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