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A279866
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Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical 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, 4, 33, 96, 255, 610, 1437, 3292, 7451, 16662, 36921, 81200, 177399, 385450, 833365, 1794180, 3848019, 8225214, 17528049, 37250392, 78966831, 167021394, 352528653, 742650796, 1561730955, 3278806630, 6873273257, 14387809152, 30078027111
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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) = 5*a(n-1) - 4*a(n-2) - 14*a(n-3) + 19*a(n-4) + 13*a(n-5) - 22*a(n-6) - 4*a(n-7) + 8*a(n-8) for n>9.
Empirical g.f.: x*(1 - x + 17*x^2 - 39*x^3 - 56*x^4 + 92*x^5 + 94*x^6 - 44*x^7 - 80*x^8) / ((1 - x)^2*(1 + x)^3*(1 - 2*x)^3). - Colin Barker, Feb 12 2019
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EXAMPLE
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Some solutions for n=4:
..0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..0. .0..1
..0..0. .1..0. .1..0. .0..0. .1..1. .0..1. .1..1. .0..1. .1..1. .2..2
..1..2. .1..1. .2..0. .0..1. .1..0. .0..1. .1..0. .0..0. .1..1. .2..2
..1..1. .1..1. .0..0. .1..1. .1..1. .0..0. .1..0. .2..2. .0..2. .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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