cp's OEIS Frontend

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.

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