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A253420
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Number of (n+2)X(4+2) nonnegative integer arrays with all values the knight distance from the upper left minus as much as 1, with successive minimum path knight move differences either 0 or +1, and any unreachable value zero.
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1
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642, 2827, 44729, 316686, 1432500, 3500244, 20832926, 31561966, 110467360, 138633628, 354021418, 407664150, 876980034, 965635182, 1845670842, 1978943526, 3471423154, 3658918494, 6009462826, 6260785942, 9758924834, 10083680846
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) for n>21.
Empirical for n mod 2 = 0: a(n) = (343040/3)*n^4 - 2458368*n^3 + (75723376/3)*n^2 - 139263620*n + 321085542 for n>12.
Empirical for n mod 2 = 1: a(n) = (343040/3)*n^4 - (6002944/3)*n^3 + (52054384/3)*n^2 - (253169804/3)*n + 171953062 for n>12.
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EXAMPLE
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Some solutions for n=2
..0..2..1..2..2..2....0..3..1..2..1..2....0..3..2..3..1..3....0..2..2..2..2..2
..2..3..1..2..2..3....2..3..1..2..2..3....2..3..1..2..2..3....3..3..1..2..2..3
..2..1..3..2..2..2....2..1..3..2..2..2....2..1..3..2..2..2....2..1..3..3..1..2
..4..2..2..2..2..3....4..1..3..2..2..3....4..1..2..1..2..3....4..2..2..1..2..3
Knight distance matrix for n=2
..0..3..2..3..2..3
..3..4..1..2..3..4
..2..1..4..3..2..3
..5..2..3..2..3..4
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CROSSREFS
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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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