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A280174
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Number of n X 2 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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1
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1, 2, 12, 41, 103, 263, 656, 1618, 3931, 9459, 22557, 53395, 125594, 293796, 683972, 1585588, 3661900, 8428646, 19341455, 44261305, 101034472, 230100558, 522936849, 1186138105, 2685582035, 6070360107, 13699764020, 30873005212, 69478759648
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OFFSET
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1,2
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-1) - 11*a(n-3) - 4*a(n-4) + 15*a(n-5) + 14*a(n-6) - 2*a(n-7) - 9*a(n-8) - 5*a(n-9) - a(n-10) for n>14.
Empirical g.f.: x*(1 - 2*x + 4*x^2 + 4*x^3 - 35*x^4 - 24*x^5 + 59*x^6 + 85*x^7 - 6*x^8 - 69*x^9 - 43*x^10 - 5*x^11 + 3*x^12 + x^13) / ((1 - x)*(1 - x - 2*x^2 - x^3)^3). - Colin Barker, Feb 13 2019
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EXAMPLE
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Some solutions for n=4:
..0..0. .0..0. .0..0. .0..1. .0..0. .0..1. .0..1. .0..1. .0..1. .0..0
..0..1. .0..0. .0..1. .1..1. .0..0. .0..1. .0..0. .0..0. .0..0. .0..1
..0..1. .0..1. .0..0. .1..1. .1..1. .0..0. .1..0. .0..0. .0..0. .0..1
..0..0. .0..1. .0..1. .0..1. .0..1. .0..0. .0..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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