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A183584 T(n,k)=Half the number of nXk 0..3 arrays with each element equal to either the maximum or the minimum of its horizontal and vertical neighbors.

%I A183584 #7 Jul 22 2025 09:06:46
%S A183584 0,2,2,2,14,2,8,78,78,8,14,407,814,407,14,38,2216,9667,9667,2216,38,
%T A183584 80,12024,110674,240358,110674,12024,80,194,65277,1282814,5987795,
%U A183584 5987795,1282814,65277,194,434,354615,14823037,149355515,320224986,149355515
%N A183584 T(n,k)=Half the number of nXk 0..3 arrays with each element equal to either the maximum or the minimum of its horizontal and vertical neighbors.
%C A183584 Table starts
%C A183584 ....0........2...........2..............8.................14
%C A183584 ....2.......14..........78............407...............2216
%C A183584 ....2.......78.........814...........9667.............110674
%C A183584 ....8......407........9667.........240358............5987795
%C A183584 ...14.....2216......110674........5987795..........320224986
%C A183584 ...38....12024.....1282814......149355515........17195908538
%C A183584 ...80....65277....14823037.....3724940988.......922710498351
%C A183584 ..194...354615...171459557....92915045150.....49526167251643
%C A183584 ..434..1926386..1982720806..2317648165893...2658141294593252
%C A183584 .1016.10465655.22929915669.57811518197886.142669482408162261
%H A183584 R. H. Hardin, <a href="/A183584/b183584.txt">Table of n, a(n) for n = 1..111</a>
%e A183584 Some solutions with a(1,1)<=1 for 4X3
%e A183584 ..1..1..3....1..3..3....1..0..3....1..2..2....0..2..2....1..2..2....1..3..3
%e A183584 ..1..3..3....1..1..1....1..0..3....1..1..3....0..0..0....1..1..3....1..0..0
%e A183584 ..2..1..3....1..1..1....0..0..0....1..1..3....0..2..2....0..3..3....1..3..3
%e A183584 ..2..1..1....2..2..2....0..1..1....1..1..1....2..2..2....0..0..3....3..3..3
%Y A183584 Column 1 is 2*A006130(n-2)
%K A183584 nonn,tabl
%O A183584 1,2
%A A183584 _R. H. Hardin_ Jan 05 2011