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A183984
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1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.
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2
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81, 83, 86, 92, 102, 122, 158, 230, 366, 638, 1166, 2222, 4302, 8462, 16718, 33230, 66126, 131918, 263246, 525902, 1050702, 2100302, 4198478, 8394830, 16785486, 33566798, 67125326, 134242382, 268468302, 536920142, 1073807438, 2147582030
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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) - 6*a(n-3) + 4*a(n-4).
G.f.: x*(81 - 160*x - 163*x^2 + 320*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = 3*2^(n/2-1) + 2^(n-1) + 78 for n even.
a(n) = 2^(n-1) + 2^((n+1)/2) + 78 for n odd.
(End)
The above empirical formula is correct. See note from Andrew Howroyd in A183986.
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EXAMPLE
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Some solutions for 5 X 8.
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....0..1..0..1..0..1..0..1
..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..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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