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A253219
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Number of n X 4 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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3, 9, 19, 19, 268, 1249, 3140, 5986, 9792, 14558, 20284, 26970, 34616, 43222, 52788, 63314, 74800, 87246, 100652, 115018, 130344, 146630, 163876, 182082, 201248, 221374, 242460, 264506, 287512, 311478, 336404, 362290, 389136, 416942, 445708
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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) = 480*n^2 - 4354*n + 10098 for n>6.
G.f.: x*(3 + x^2 - 14*x^3 + 259*x^4 + 483*x^5 + 178*x^6 + 45*x^7 + 5*x^8) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)
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EXAMPLE
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Some solutions for n=4:
..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..1....0..0..0..1
..0..0..1..1....0..1..1..1....0..0..1..1....0..0..0..1....0..0..0..1
..1..1..1..1....1..1..1..1....0..0..1..1....0..0..1..1....1..1..1..1
..1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
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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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