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A253507
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Number of (n+2) X (5+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.
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1
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884, 1712, 3052, 5136, 7948, 11740, 16592, 22720, 30300, 39560, 50740, 64104, 79936, 98540, 120240, 145380, 174324, 207456, 245180, 287920, 336120, 390244, 450776, 518220, 593100, 675960, 767364, 867896, 978160, 1098780, 1230400, 1373684
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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) = (5/6)*n^4 + 9*n^3 + (1135/6)*n^2 + 361*n - 300 for n>8.
G.f.: 4*x*(221 - 677*x + 833*x^2 - 461*x^3 + 22*x^4 + 129*x^5 - 110*x^6 + 77*x^7 - 44*x^8 + 23*x^9 - 10*x^10 + 3*x^11 - x^12) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>13.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1..1..1..1..1..1....0..1..1..1..1..1..1....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..0..0..0
..1..1..1..1..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
..1..1..1..1..1..1..0....1..1..1..1..1..0..1....1..1..1..0..0..0..0
..1..1..1..1..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
..1..1..1..0..0..0..0....0..0..0..0..1..0..1....1..1..0..0..0..0..0
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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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