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A189450
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Number of 2 X n array permutations with each element moving zero or one space horizontally or diagonally.
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1
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1, 5, 16, 61, 225, 841, 3136, 11705, 43681, 163021, 608400, 2270581, 8473921, 31625105, 118026496, 440480881, 1643897025, 6135107221, 22896531856, 85451020205, 318907548961, 1190179175641, 4441809153600, 16577057438761
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-1) -4*a(n-3) +a(n-4).
G.f.: x*(1 + x - 4*x^2 + x^3) / ((1 - x)*(1 + x)*(1 - 4*x + x^2)).
a(n) = ((2-sqrt(3))^(n+1) + (2+sqrt(3))^(n+1) + 8) / 12 for n even.
a(n) = (-2+(2-sqrt(3))^(1+n) + (2+sqrt(3))^(1+n)) / 12 for n odd.
(End)
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EXAMPLE
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Some solutions for 2 X 3:
..4..5..2....0..5..2....0..1..2....1..0..2....0..2..1....0..1..2....4..2..1
..3..0..1....3..4..1....4..3..5....4..3..5....3..4..5....3..4..5....3..0..5
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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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