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A263520
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Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.
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1
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8, 35, 160, 660, 2651, 10350, 39807, 151463, 572454, 2153977, 8081566, 30264786, 113201857, 423085492, 1580453125, 5901900685, 22034817900, 82255893847, 307033492332, 1145986101448, 4277171754383, 15963330711354, 59577671664211
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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) = 7*a(n-1) - 11*a(n-2) - 14*a(n-3) + 36*a(n-4) + 8*a(n-5) - 36*a(n-6) - 2*a(n-7) + 13*a(n-8) + a(n-9) - a(n-10).
Empirical g.f.: x*(8 - 21*x + 3*x^2 + 37*x^3 - 7*x^4 - 31*x^5 + 6*x^6 + 14*x^7 - x^9) / ((1 - x)^2*(1 + x)^2*(1 - 4*x + x^2)*(1 - x - x^2)*(1 - 2*x - x^2)). - Colin Barker, Jan 01 2019
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EXAMPLE
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Some solutions for n=4:
..0..1..2..8..9....0..1..2..4..9....0..1..2..3..4....0..2..3..4..9
.10..5..7..3..4....5..6..8..3.14....5..6.12..7.14....5..1..6..7..8
.11..6.12.14.13...11.10..7.12.13...11.10.13..8..9...10.11.13.12.14
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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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