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A224411
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Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.
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1
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16, 108, 358, 884, 1928, 3902, 7490, 13784, 24467, 42053, 70195, 114073, 180875, 280385, 425693, 634043, 927836, 1335806, 1894388, 2649298, 3657346, 4988504, 6728252, 8980226, 11869193, 15544379, 20183177, 25995263, 33227149, 42167203
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (31/2880)*n^6 + (13/144)*n^5 + (3767/5760)*n^4 + (6409/1440)*n^3 + (189859/10080)*n^2 - (73/24)*n - 7 for n>2.
G.f.: x*(16 - 36*x - 38*x^2 + 206*x^3 - 196*x^4 - 106*x^5 + 368*x^6 - 334*x^7 + 155*x^8 - 38*x^9 + 4*x^10) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..0..0....0..0..0....0..0..0....1..0..0....0..0..0....1..1..0....0..0..0
..0..0..1....0..0..0....1..1..0....0..1..1....1..1..0....1..1..0....1..0..0
..0..1..0....1..1..1....1..1..1....1..1..1....1..0..0....1..1..0....0..1..0
..1..0..0....1..1..1....1..1..1....1..1..0....0..1..0....1..0..0....1..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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