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A014524
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Number of Hamiltonian paths from NW to SW corners in a grid with 2n rows and 4 columns.
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5
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0, 1, 8, 47, 264, 1480, 8305, 46616, 261663, 1468752, 8244304, 46276385, 259755560, 1458042831, 8184190168, 45938958232, 257861540369, 1447411446840, 8124514782015, 45603992276896, 255981331487648
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 7*a(n-1)-9*a(n-2)+7*a(n-3)-a(n-4).
G.f.: x*(x+1)/(x^4-7*x^3+9*x^2-7*x+1). (End)
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EXAMPLE
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Illustration of a(1)=1:
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Illustration of a few of the 8 solutions to a(2):
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|__ | | |__| |__. .__. |__. |__.__.__.
.__| |__| .__.__.__| | |__.__| .__.__.__|
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MATHEMATICA
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CoefficientList[Series[x (x + 1)/(x^4 - 7 x^3 + 9 x^2 - 7 x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
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CROSSREFS
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Even bisection of column 4 of A271592.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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