A183388 Half the number of n X 4 binary arrays with no element unequal to a strict majority of its king-move neighbors.

2, 2, 2, 4, 8, 16, 36, 74, 156, 334, 706, 1504, 3204, 6828, 14576, 31128, 66524, 142262, 304360, 651456, 1394894, 2987672, 6400950, 13716916, 29400542, 63027304, 135134330, 289772558, 621434722, 1332826866, 2858815828, 6132363430

Offset

1,1

Comments

Column 4 of A183391.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) - 4*a(n-4) - 3*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) for n>9.

Empirical g.f.: 2*x*(1 - x - 3*x^2 - x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 2*x^7 - 2*x^8) / (1 - 2*x - 2*x^2 + x^3 + 4*x^4 + 3*x^5 + x^6 + x^7 - 2*x^8). - Colin Barker, Mar 28 2018

Example

Some solutions with a(1,1)=0 for 5 X 4:
..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
..1..1..0..0....0..0..1..1....1..1..1..1....0..0..1..1....0..0..1..1
..1..1..0..0....0..0..1..1....1..1..1..1....1..1..0..0....1..1..1..1
..1..1..0..0....0..0..1..1....1..1..1..1....1..1..0..0....1..1..1..1

Crossrefs

Cf. A183391.

Sequence in context: A285636 A102831 A262568 * A274076 A160179 A021822

Adjacent sequences: A183385 A183386 A183387 * A183389 A183390 A183391

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved