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

1,5

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

Links

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

Example

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

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).

Sequence in context: A049992 A227147 A074585 * A108038 A151845 A230448

Adjacent sequences: A183309 A183310 A183311 * A183313 A183314 A183315

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2011

Status

approved