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A253500
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Number of (6+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
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1
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19701, 22236, 29370, 40117, 63550, 113573, 220988, 457436, 995132, 2264924, 5387708, 13382876, 34622012, 92846684, 256535228, 725629916, 2088972092, 6091114844, 17921775548, 53062222556, 157780493372, 470529165404
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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) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.
Empirical: a(n) = 400*3^(n-3) + 2682*2^(n-1) + 16940 for n>6.
Empirical g.f.: x*(19701 - 95970*x + 112665*x^2 - 9713*x^3 + 12502*x^4 - 2660*x^5 - 2102*x^6 - 489*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Dec 16 2018
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EXAMPLE
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Some solutions for n=4:
..1..2..2..2..2....0..0..0..1..0....0..1..0..0..0....1..1..2..1..2
..2..2..2..2..2....1..1..1..2..1....0..1..0..0..0....1..0..1..0..1
..0..0..0..0..0....0..0..0..1..0....1..2..1..1..1....1..0..1..0..1
..2..2..2..2..2....0..0..0..1..0....0..1..0..0..0....1..0..1..0..1
..2..2..2..2..2....0..0..0..1..0....1..2..1..1..1....1..0..1..0..1
..1..1..1..1..1....0..0..0..1..0....0..1..0..0..0....1..0..1..0..1
..1..1..1..1..1....0..0..0..2..2....0..1..0..0..2....1..0..1..0..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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