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A253220
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Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
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1
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6, 25, 102, 268, 268, 3568, 16028, 40238, 77063, 126673, 189083, 264293, 352303, 453113, 566723, 693133, 832343, 984353, 1149163, 1326773, 1517183, 1720393, 1936403, 2165213, 2406823, 2661233, 2928443, 3208453, 3501263, 3806873, 4125283
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 6400*n^2 - 71990*n + 206573 for n>8.
G.f.: x*(6 + 7*x + 45*x^2 + 31*x^3 - 255*x^4 + 3466*x^5 + 5860*x^6 + 2590*x^7 + 865*x^8 + 170*x^9 + 15*x^10) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..1..1..1..2....0..1..1..2..2....0..0..0..1..2....0..0..0..1..2
..1..1..1..1..2....0..1..1..2..2....0..0..0..1..2....1..1..1..1..2
..1..1..2..2..2....1..1..2..2..2....0..1..1..1..2....1..1..2..2..2
..1..2..2..2..2....2..2..2..2..2....1..1..2..2..2....2..2..2..2..2
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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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