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A279865
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Number of n X 1 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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3
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0, 1, 0, 6, 6, 30, 54, 158, 342, 846, 1910, 4446, 10038, 22734, 50838, 113310, 250774, 552654, 1211958, 2647390, 5760630, 12492366, 27003990, 58202526, 125104086, 268228430, 573739254, 1224529758, 2608132022, 5544352206, 11764763670
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OFFSET
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1,4
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COMMENTS
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Column 1 of A279871.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6).
Conjectures from Colin Barker, Feb 26 2018: (Start)
G.f.: x^2*(1 - x)^3 / ((1 + x)^3*(1 - 2*x)^3).
a(n) = (3*2^n*n^2 + 96*n^2 + 21*2^n*n + 2^(n+4) - 16) / 648 for n even.
a(n) = (3*2^n*n^2 - 96*n^2 + 21*2^n*n + 2^(n+4) + 16) / 648 for n odd.
(End)
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EXAMPLE
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All solutions for n=4:
..0. .0. .0. .0. .0. .0
..1. .0. .1. .0. .1. .1
..1. .1. .0. .1. .1. .2
..0. .2. .0. .0. .2. .2
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CROSSREFS
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Cf. A279871.
Sequence in context: A078637 A147799 A071021 * A321528 A074002 A359741
Adjacent sequences: A279862 A279863 A279864 * A279866 A279867 A279868
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Dec 21 2016
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STATUS
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approved
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