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A221788
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Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without 2-loops or left turns.
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1
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0, 0, 0, 5, 24, 142, 840, 4919, 28704, 167344, 975408, 5685161, 33135624, 193128658, 1125636408, 6560689883, 38238502992, 222870328180, 1298983466208, 7571030469197, 44127199349112, 257192165625622, 1499025794404776
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 8*a(n-1) - 14*a(n-2) + 8*a(n-3) - a(n-4) for n>6.
G.f.: x^4*(5 - 16*x + 20*x^2) / ((1 - x)^2*(1 - 6*x + x^2)).
a(n) = (408 + sqrt(2)*((10041-7100*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(10041+7100*sqrt(2))) - 72*(1+n)) / 32 for n>2.
(End)
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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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