A183393 Half the number of n X 2 binary arrays with no element equal to a strict majority of its knight-move neighbors.

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

R. H. Hardin, Table of n, a(n) for n = 1..200

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

Adjacent sequences: A183390 A183391 A183392 * A183394 A183395 A183396

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved