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A186168 T(n,k)=1/4 the number of nXk 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A186168 #7 Jul 22 2025 10:17:34
%S A186168 0,1,1,1,7,1,4,48,48,4,7,321,702,321,7,19,2175,14364,14364,2175,19,40,
%T A186168 14748,253341,751266,253341,14748,40,97,99933,4762206,37402872,
%U A186168 37402872,4762206,99933,97,217,677283,87054174,1899336597,5033988714,1899336597
%N A186168 T(n,k)=1/4 the number of nXk 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A186168 Table starts
%C A186168 ...0........1............1...............4.................7.................19
%C A186168 ...1........7...........48.............321..............2175..............14748
%C A186168 ...1.......48..........702...........14364............253341............4762206
%C A186168 ...4......321........14364..........751266..........37402872.........1899336597
%C A186168 ...7.....2175.......253341........37402872........5033988714.......704281652979
%C A186168 ..19....14748......4762206......1899336597......704281652979....268995986029278
%C A186168 ..40....99933.....87054174.....95752776009....96951738076992.101554003879403823
%C A186168 ..97...677283...1610684397...4840082975532.13435825601048421
%C A186168 .217..4590168..29645381115.244420512852030
%C A186168 .508.31108893.546876640548
%H A186168 R. H. Hardin, <a href="/A186168/b186168.txt">Table of n, a(n) for n = 1..84</a>
%e A186168 Some solutions for 5X4 with a(1,1)=0
%e A186168 ..0..0..1..0....0..0..1..1....0..0..1..1....0..0..1..0....0..0..1..1
%e A186168 ..0..0..1..0....0..0..3..2....0..0..2..2....0..0..1..0....0..0..2..1
%e A186168 ..1..1..3..3....1..1..3..2....1..1..0..0....1..1..0..0....1..1..2..2
%e A186168 ..0..0..3..3....0..1..3..2....1..3..3..0....1..1..2..1....2..2..1..0
%e A186168 ..1..1..0..0....0..0..0..0....0..0..2..2....0..0..2..1....3..3..1..0
%Y A186168 Column 1 is A006130(n-2)
%K A186168 nonn,tabl
%O A186168 1,5
%A A186168 _R. H. Hardin_ Feb 13 2011