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%I #9 Dec 26 2023 16:38:46
%S 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,
%T 93,178,178,93,22,13,21,35,205,572,910,572,205,35,21,34,56,452,1798,
%U 4212,4212,1798,452,56,34,55,90,997,5700,19899,29400,19899,5700,997,90,55,89
%N 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.
%C Same solutions for no element unequal to a strict majority of its horizontal and vertical neighbors, via xor with a 0101... checkerboard pattern.
%C Table starts
%C ..1..1....1.....2.......3........5..........8..........13............21
%C ..1..3....4.....6.......9.......14.........22..........35............56
%C ..1..4....9....19......42.......93........205.........452...........997
%C ..2..6...19....55.....178......572.......1798........5700.........18064
%C ..3..9...42...178.....910.....4212......19899.......94217........445859
%C ..5.14...93...572....4212....29400.....206755.....1447110......10149621
%C ..8.22..205..1798...19899...206755....2160250....22504107.....234636215
%C .13.35..452..5700...94217..1447110...22504107...348871589....5406312318
%C .21.56..997.18064..445859.10149621..234636215..5406312318..124597748299
%C .34.90.2199.57249.2113257.71244598.2447317278.83828453334.2872365166632
%H R. H. Hardin, <a href="/A183312/b183312.txt">Table of n, a(n) for n = 1..337</a>
%e Some solutions with a(1,1)=0 for 6 X 6
%e ..0..1..0..1..0..0....0..1..1..0..0..1....0..1..1..0..0..1....0..1..0..1..0..0
%e ..1..1..0..0..1..1....1..0..0..1..1..0....1..0..0..1..1..0....0..1..1..0..1..1
%e ..0..0..1..1..0..0....0..1..0..0..1..0....0..0..1..0..0..1....1..0..1..1..0..0
%e ..1..1..1..0..1..1....0..1..1..0..0..1....1..1..0..1..1..0....0..1..0..0..1..1
%e ..0..0..0..1..0..0....1..0..0..1..0..0....0..1..0..0..1..0....1..0..0..1..0..0
%e ..1..1..0..1..0..1....0..1..1..0..1..1....1..0..1..1..0..1....1..0..1..0..1..1
%Y Column 1 is A000045(n-1) for n>1.
%Y Column 2 is A000045(n+1)+1 for n>1.
%Y Cf. A183304 (col 3), A183305 (col 4), A183306 (col 5), A183307 (col 6), A183308 (col 7), A183309 (col 8).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 03 2011
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