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A196685 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

%I A196685 #7 Jun 02 2025 04:30:32
%S A196685 1,3,3,4,9,4,5,20,20,5,9,61,58,61,9,16,189,292,292,189,16,25,544,1235,
%T A196685 2245,1235,544,25,39,1629,5186,15395,15395,5186,1629,39,64,4973,22461,
%U A196685 109528,188078,109528,22461,4973,64,105,15040,96256,796557,2169685
%N A196685 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.
%C A196685 Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 3's
%C A196685 Table starts
%C A196685 ...1.....3.......4.........5...........9............16..............25
%C A196685 ...3.....9......20........61.........189...........544............1629
%C A196685 ...4....20......58.......292........1235..........5186...........22461
%C A196685 ...5....61.....292......2245.......15395........109528..........796557
%C A196685 ...9...189....1235.....15395......188078.......2169685........25142624
%C A196685 ..16...544....5186....109528.....2169685......39696088.......741925729
%C A196685 ..25..1629...22461....796557....25142624.....741925729.....23029545105
%C A196685 ..39..4973...96256...5702355...291420839...14189246566....718199634805
%C A196685 ..64.15040..413032..40479328..3417608122..269528695666..22138818455076
%C A196685 .105.45739.1780597.289195575.40048090008.5096101360077.682005890331480
%H A196685 R. H. Hardin, <a href="/A196685/b196685.txt">Table of n, a(n) for n = 1..144</a>
%e A196685 Some solutions for n=6 k=4
%e A196685 ..0..0..1..1....1..1..0..1....0..0..0..1....0..0..0..0....1..0..0..0
%e A196685 ..1..1..2..0....0..1..1..1....0..0..0..2....1..1..2..0....1..2..1..1
%e A196685 ..2..1..0..0....0..1..1..0....0..0..0..1....2..2..1..0....0..2..1..2
%e A196685 ..0..1..2..0....0..1..1..0....1..2..1..2....1..2..2..0....1..1..0..0
%e A196685 ..2..1..1..0....0..2..1..0....1..0..2..0....0..1..1..2....1..1..0..0
%e A196685 ..1..0..2..1....0..0..2..1....2..1..1..0....1..2..0..1....0..1..2..1
%Y A196685 Column 1 is A195971
%Y A196685 Column 2 is A196212
%K A196685 nonn,tabl
%O A196685 1,2
%A A196685 _R. H. Hardin_ Oct 05 2011