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A197409 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 3,0,1,1,1 for x=0,1,2,3,4.

%I A197409 #7 Jun 02 2025 04:54:25
%S A197409 1,3,3,4,9,4,5,20,20,5,9,71,60,71,9,16,227,358,358,227,16,25,664,1626,
%T A197409 3305,1626,664,25,39,2107,7232,25621,25621,7232,2107,39,64,6675,34717,
%U A197409 199384,356211,199384,34717,6675,64,105,20696,160988,1634731,4499426
%N A197409 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 3,0,1,1,1 for x=0,1,2,3,4.
%C A197409 Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
%C A197409 Table starts
%C A197409 ...1.....3.......4.........5............9.............16...............25
%C A197409 ...3.....9......20........71..........227............664.............2107
%C A197409 ...4....20......60.......358.........1626...........7232............34717
%C A197409 ...5....71.....358......3305........25621.........199384..........1634731
%C A197409 ...9...227....1626.....25621.......356211........4499426.........60334353
%C A197409 ..16...664....7232....199384......4499426.......93153650.......2065093081
%C A197409 ..25..2107...34717...1634731.....60334353.....2065093081......77683473682
%C A197409 ..39..6675..160988..13013551....801294395....45796265386....2861267797023
%C A197409 ..64.20696..748843.103260478..10631272297..1003308210971..104224692369107
%C A197409 .105.65029.3514426.825286477.141478252511.22026879283832.3821001855576417
%H A197409 R. H. Hardin, <a href="/A197409/b197409.txt">Table of n, a(n) for n = 1..144</a>
%e A197409 Some solutions containing all values 0 to 4 for n=6 k=4
%e A197409 ..0..1..1..0....2..1..2..0....2..1..1..0....1..0..1..2....2..1..2..0
%e A197409 ..0..2..2..1....1..0..1..1....1..0..2..0....1..0..1..1....1..0..1..1
%e A197409 ..0..1..3..1....1..0..1..3....1..0..1..1....1..0..2..0....3..1..4..1
%e A197409 ..1..4..1..0....1..1..4..1....2..1..4..1....3..1..1..0....1..4..1..0
%e A197409 ..1..1..1..2....0..1..1..0....0..1..1..0....1..4..1..0....0..1..1..0
%e A197409 ..0..0..0..1....1..3..1..0....1..3..1..0....0..1..2..0....1..3..1..0
%Y A197409 Column 1 is A195971
%K A197409 nonn,tabl
%O A197409 1,2
%A A197409 _R. H. Hardin_ Oct 14 2011