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A183368 T(n,k)=Number of nXk binary arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors.

%I A183368 #7 Jul 22 2025 08:52:25
%S A183368 1,2,2,2,3,2,3,5,5,3,4,12,18,12,4,5,21,39,39,21,5,7,41,108,138,108,41,
%T A183368 7,9,84,288,548,548,288,84,9,12,171,795,2129,3102,2129,795,171,12,16,
%U A183368 355,2278,8311,17101,17101,8311,2278,355,16,21,732,6438,32933,95674,137688
%N A183368 T(n,k)=Number of nXk binary arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors.
%C A183368 Table starts
%C A183368 ..1...2.....2......3........4.........5...........7............9.............12
%C A183368 ..2...3.....5.....12.......21........41..........84..........171............355
%C A183368 ..2...5....18.....39......108.......288.........795.........2278...........6438
%C A183368 ..3..12....39....138......548......2129........8311........32933.........130750
%C A183368 ..4..21...108....548.....3102.....17101.......95674.......543837........3094889
%C A183368 ..5..41...288...2129....17101....137688.....1107441......8969225.......72989578
%C A183368 ..7..84...795...8311....95674...1107441....12617557....145766281.....1687526938
%C A183368 ..9.171..2278..32933...543837...8969225...145766281...2402945556....39693410307
%C A183368 .12.355..6438.130750..3094889..72989578..1687526938..39693410307...936460285557
%C A183368 .16.732.18394.519980.17654882.594531764.19534278264.655471213213.22047188457210
%H A183368 R. H. Hardin, <a href="/A183368/b183368.txt">Table of n, a(n) for n = 1..199</a>
%e A183368 Some solutions for 6X5
%e A183368 ..0..1..0..0..1....1..1..1..0..1....0..0..1..1..1....1..1..1..1..1
%e A183368 ..0..0..0..0..0....1..0..1..0..0....1..0..1..0..1....1..0..1..0..1
%e A183368 ..1..1..1..1..1....1..1..1..0..1....0..0..1..1..1....1..1..1..1..1
%e A183368 ..1..1..0..1..1....1..1..1..0..0....0..1..1..0..1....0..0..0..0..0
%e A183368 ..0..0..1..0..0....1..0..1..1..0....1..1..0..1..1....1..1..1..0..0
%e A183368 ..1..0..0..0..1....1..1..1..1..0....1..1..1..1..0....1..1..1..0..1
%Y A183368 Column 1 is A000931(n+6)
%K A183368 nonn,tabl
%O A183368 1,2
%A A183368 _R. H. Hardin_ Jan 04 2011