A183312 T(n,k) = Half the number of n X k binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors.

1, 1, 1, 1, 3, 1, 2, 4, 4, 2, 3, 6, 9, 6, 3, 5, 9, 19, 19, 9, 5, 8, 14, 42, 55, 42, 14, 8, 13, 22, 93, 178, 178, 93, 22, 13, 21, 35, 205, 572, 910, 572, 205, 35, 21, 34, 56, 452, 1798, 4212, 4212, 1798, 452, 56, 34, 55, 90, 997, 5700, 19899, 29400, 19899, 5700, 997, 90, 55, 89

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn
• tabl

Comments

Same solutions for no element unequal to a strict majority of its horizontal and vertical neighbors, via xor with a 0101... checkerboard pattern.

Table starts

..1..1....1.....2.......3........5..........8..........13............21

..1..3....4.....6.......9.......14.........22..........35............56

..1..4....9....19......42.......93........205.........452...........997

..2..6...19....55.....178......572.......1798........5700.........18064

..3..9...42...178.....910.....4212......19899.......94217........445859

..5.14...93...572....4212....29400.....206755.....1447110......10149621

..8.22..205..1798...19899...206755....2160250....22504107.....234636215

.13.35..452..5700...94217..1447110...22504107...348871589....5406312318

.21.56..997.18064..445859.10149621..234636215..5406312318..124597748299

.34.90.2199.57249.2113257.71244598.2447317278.83828453334.2872365166632

Examples

			Some solutions with a(1,1)=0 for 6 X 6
..0..1..0..1..0..0....0..1..1..0..0..1....0..1..1..0..0..1....0..1..0..1..0..0
..1..1..0..0..1..1....1..0..0..1..1..0....1..0..0..1..1..0....0..1..1..0..1..1
..0..0..1..1..0..0....0..1..0..0..1..0....0..0..1..0..0..1....1..0..1..1..0..0
..1..1..1..0..1..1....0..1..1..0..0..1....1..1..0..1..1..0....0..1..0..0..1..1
..0..0..0..1..0..0....1..0..0..1..0..0....0..1..0..0..1..0....1..0..0..1..0..0
..1..1..0..1..0..1....0..1..1..0..1..1....1..0..1..1..0..1....1..0..1..0..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..337

Crossrefs

Column 1 is A000045(n-1) for n>1.

Column 2 is A000045(n+1)+1 for n>1.

Cf. A183304 (col 3), A183305 (col 4), A183306 (col 5), A183307 (col 6), A183308 (col 7), A183309 (col 8).