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A223839
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Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
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1
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4, 16, 48, 118, 255, 503, 926, 1614, 2690, 4318, 6712, 10146, 14965, 21597, 30566, 42506, 58176, 78476, 104464, 137374, 178635, 229891, 293022, 370166, 463742, 576474, 711416, 871978, 1061953, 1285545, 1547398, 1852626, 2206844, 2616200
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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) = (1/720)*n^6 + (1/240)*n^5 + (29/144)*n^4 + (11/48)*n^3 + (1007/360)*n^2 - (37/30)*n + 2.
G.f.: x*(2 - 2*x + x^2)*(2 - 4*x + 5*x^2 - 4*x^3 + 2*x^4) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
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EXAMPLE
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Some solutions for n=3:
..1..1..0....0..0..0....0..1..0....1..0..0....1..0..0....0..1..0....0..1..1
..1..1..0....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..1
..1..1..1....0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1
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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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