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A183393
Half the number of n X 2 binary arrays with no element equal to a strict majority of its knight-move neighbors.
1
2, 8, 8, 8, 8, 8, 32, 128, 288, 648, 1800, 5000, 12800, 32768, 86528, 228488, 596232, 1555848, 4078368, 10690688, 27975200, 73205000, 191688200, 501937928, 1313998848, 3439853568, 9005893632, 23578364168, 61728330248, 161605221128
OFFSET
1,1
COMMENTS
Column 2 of A183397.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 6*a(n-3) - 6*a(n-5) + 3*a(n-6) - 3*a(n-7) + a(n-8) for n>11.
Empirical g.f.: 2*x*(1 + x - 5*x^2 - 2*x^3 - 20*x^4 - 14*x^5 + 13*x^6 + 19*x^7 - x^8 + 8*x^9 - 4*x^10) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + 3*x^2 + x^4)). - Colin Barker, Mar 28 2018
EXAMPLE
Some solutions with a(1,1)=0 for 10 X 2:
..0..1....0..1....0..0....0..1....0..0....0..0....0..0....0..1....0..1....0..0
..0..1....0..0....1..1....1..0....1..0....0..0....0..0....0..1....1..1....1..1
..0..1....0..1....1..1....0..1....1..1....1..1....1..1....0..1....0..1....1..1
..0..1....1..1....0..0....1..0....1..0....1..1....1..1....0..1....0..0....0..0
..1..0....0..1....0..0....0..1....0..1....1..0....1..0....1..1....1..1....1..1
..0..1....0..0....1..0....1..0....1..0....0..0....1..0....0..1....1..0....1..1
..1..0....0..1....1..0....0..0....0..1....0..0....1..0....1..0....0..0....0..0
..0..1....1..0....1..0....1..0....1..0....1..1....1..0....1..1....1..1....1..1
..1..0....0..1....1..0....1..1....0..1....1..1....1..0....1..0....1..1....1..1
..0..1....1..0....1..0....1..0....1..0....0..0....1..0....0..0....0..0....0..0
CROSSREFS
Cf. A183397.
Sequence in context: A138300 A137575 A360780 * A284781 A289841 A143812
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 04 2011
STATUS
approved