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A225895
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Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.
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1
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7, 33, 145, 545, 1770, 5052, 12910, 30055, 64701, 130387, 248427, 451117, 785840, 1320222, 2148504, 3399307, 5244979, 7912725, 11697733, 16978521, 24234742, 34067696, 47223810, 64621359, 87380713, 116858407, 154685343, 202809445
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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) = (1/3360)*n^8 + (3/560)*n^7 + (5/144)*n^6 + (7/120)*n^5 + (761/1440)*n^4 + (81/80)*n^3 + (122/63)*n^2 + (89/210)*n + 3.
G.f.: x*(7 - 30*x + 100*x^2 - 160*x^3 + 195*x^4 - 162*x^5 + 82*x^6 - 23*x^7 + 3*x^8) / (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>9.
(End)
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EXAMPLE
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Some solutions for n=3:
..0..0..1....0..1..1....0..0..0....0..0..1....0..0..1....0..0..1....0..0..0
..0..1..0....1..0..0....1..1..0....1..0..0....1..1..0....0..0..1....0..0..1
..1..0..0....1..1..1....1..1..0....1..0..0....1..1..1....1..0..0....1..1..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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