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A225977
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Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.
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1
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8, 48, 252, 1178, 4722, 16361, 49811, 135672, 336189, 768900, 1642668, 3310404, 6343682, 11635425, 20537903, 35044430, 58024377, 93522432, 147134436, 226473606, 341742522, 506427905, 738136947, 1059595772, 1499832509
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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) = (1/4320)*n^9 + (23/6720)*n^8 + (5/336)*n^7 - (1/288)*n^6 + (659/1440)*n^5 + (443/2880)*n^4 + (80/27)*n^3 - (6203/1008)*n^2 + (2459/140)*n - 6 for n>1.
G.f.: x*(8 - 32*x + 132*x^2 - 142*x^3 + 202*x^4 - 25*x^5 - 165*x^6 + 163*x^7 - 72*x^8 + 16*x^9 - x^10) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..1....0..1..1
..1..0..0....0..1..0....1..1..1....1..0..1....0..1..0....0..1..0....0..0..1
..1..1..1....0..1..1....0..1..0....0..0..1....0..0..1....0..1..1....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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