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A227162
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Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
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1
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4, 18, 62, 193, 558, 1507, 3828, 9149, 20609, 43918, 88960, 172130, 319637, 572050, 990413, 1664308, 2722302, 4345275, 6783191, 10375943, 15578976, 22994469, 33408938, 47838207, 67580783, 94280764, 130001506, 177311376, 239383023
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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) = (1/90720)*n^9 + (1/8064)*n^8 + (17/30240)*n^7 + (13/960)*n^6 - (131/4320)*n^5 + (181/384)*n^4 - (146161/90720)*n^3 + (171511/10080)*n^2 - (25129/504)*n + 58 for n>3.
G.f.: x*(4 - 22*x + 62*x^2 - 97*x^3 + 98*x^4 - 56*x^5 + 32*x^6 - 70*x^7 + 123*x^8 - 113*x^9 + 55*x^10 - 13*x^11 + x^12) / (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>13.
(End)
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EXAMPLE
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Some solutions for n=4:
..1..1..1....1..1..1....1..0..0....1..0..0....1..0..0....0..0..0....0..0..0
..1..1..0....1..1..1....0..0..1....0..0..1....0..0..0....0..1..1....0..1..1
..1..1..0....1..1..1....0..0..1....0..0..0....0..0..1....0..1..1....0..1..0
..1..0..0....1..1..0....0..0..0....0..0..0....0..0..1....0..1..0....0..0..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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