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A201373
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Number of n X 6 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
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1
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2, 7, 32, 157, 786, 3739, 15574, 55410, 170616, 465037, 1145954, 2597729, 5492076, 10947133, 20749996, 37660122, 65814022, 111254955, 182614908, 291980013, 455974718, 697104503, 1045401722, 1540424266, 2233662188, 3191413217
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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) = (1/453600)*n^10 + (1/2160)*n^9 + (227/60480)*n^8 - (73/1260)*n^7 + (1319/10800)*n^6 + (757/720)*n^5 - (881131/181440)*n^4 + (2207/540)*n^3 + (396407/25200)*n^2 - (6737/210)*n + 18.
G.f.: x*(2 - 15*x + 65*x^2 - 140*x^3 + 324*x^4 - 166*x^5 + 20*x^6 - 349*x^7 + 391*x^8 - 142*x^9 + 18*x^10) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
(End)
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EXAMPLE
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Some solutions for n=5:
..0..0..0..1..1..1....0..0..0..1..1..1....0..0..0..0..1..1....0..0..1..1..1..1
..1..1..1..0..1..1....1..1..1..0..1..1....0..1..1..1..0..1....0..0..1..1..1..1
..1..1..1..1..0..1....1..1..1..1..0..1....1..0..0..1..0..1....0..1..0..1..1..1
..1..1..1..1..1..0....1..1..1..1..0..1....1..0..0..1..1..0....1..0..0..1..1..1
..1..1..1..1..1..0....1..1..1..1..1..0....1..1..1..0..0..0....1..1..1..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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