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A230929
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Number of black-square subarrays of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
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2
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2, 6, 16, 48, 146, 438, 1312, 3936, 11810, 35430, 106288, 318864, 956594, 2869782, 8609344, 25828032, 77484098, 232452294, 697356880, 2092070640, 6276211922, 18828635766, 56485907296, 169457721888, 508373165666, 1525119496998
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3).
Empirical g.f.: 2*x / ((1 - 3*x)*(1 + x^2)). - Colin Barker, Mar 17 2018
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EXAMPLE
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Some solutions for n=4:
..x..0..x..2....x..0..x..0....x..0..x..2....x..0..x..2....x..0..x..0
..1..x..3..x....3..x..1..x....1..x..3..x....1..x..3..x....1..x..1..x
..x..2..x..2....x..2..x..3....x..2..x..0....x..2..x..2....x..2..x..2
..1..x..3..x....0..x..0..x....3..x..1..x....3..x..3..x....3..x..3..x
..x..0..x..2....x..1..x..3....x..0..x..0....x..0..x..2....x..0..x..2
..3..x..1..x....0..x..2..x....3..x..3..x....3..x..1..x....3..x..1..x
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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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