A183389 Half the number of n X 5 binary arrays with no element unequal to a strict majority of its king-move neighbors.

3, 3, 3, 8, 21, 49, 136, 355, 933, 2502, 6653, 17823, 47798, 128301, 344943, 927972, 2498033, 6728001, 18126410, 48849585, 131672723, 354973646, 957076001, 2580677445, 6959034768, 18766590985, 50610139265, 136490237350, 368107422167

Offset

1,1

Comments

Column 5 of A183391.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 4*a(n-3) - 11*a(n-4) - 3*a(n-5) + 4*a(n-6) - 8*a(n-7) + 10*a(n-9) - 2*a(n-10) - a(n-11) for n>12.

Empirical g.f.: x*(3 - 3*x - 18*x^2 - x^3 + 35*x^4 + 21*x^5 - 5*x^6 + 31*x^7 + 6*x^8 - 31*x^9 + 3*x^10 + 3*x^11) / (1 - 2*x - 5*x^2 + 4*x^3 + 11*x^4 + 3*x^5 - 4*x^6 + 8*x^7 - 10*x^9 + 2*x^10 + x^11). - Colin Barker, Mar 28 2018

Example

Some solutions with a(1,1)=0 for 7 X 5:
..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..1....0..0..0..0..0....1..1..0..0..0....1..1..1..0..0
..0..0..0..0..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
..0..0..0..1..1....0..0..1..1..1....0..0..1..1..1....0..0..1..1..1
..0..0..0..1..1....1..1..1..1..1....0..0..0..1..1....0..0..0..0..0
..0..0..0..1..1....1..1..1..1..1....0..0..0..1..1....0..0..0..0..0

Crossrefs

Cf. A183391.

Sequence in context: A241739 A226509 A329694 * A275530 A180637 A362376

Adjacent sequences: A183386 A183387 A183388 * A183390 A183391 A183392

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved