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A198185 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 0,2,1,0,0 for x=0,1,2,3,4.

%I A198185 #7 Jun 02 2025 05:24:16
%S A198185 1,0,0,1,4,1,2,3,3,2,1,8,9,8,1,1,16,25,25,16,1,3,21,77,59,77,21,3,3,
%T A198185 56,148,331,331,148,56,3,2,70,395,883,2033,883,395,70,2,4,171,866,
%U A198185 3485,8298,8298,3485,866,171,4,6,256,2346,12030,48958,51688,48958,12030,2346,256,6
%N A198185 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 0,2,1,0,0 for x=0,1,2,3,4.
%C A198185 Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's
%C A198185 Table starts
%C A198185 .1...0....1......2.......1.........1..........3............3.............2
%C A198185 .0...4....3......8......16........21.........56...........70...........171
%C A198185 .1...3....9.....25......77.......148........395..........866..........2346
%C A198185 .2...8...25.....59.....331.......883.......3485........12030.........43774
%C A198185 .1..16...77....331....2033......8298......48958.......216307.......1155412
%C A198185 .1..21..148....883....8298.....51688.....395340......2639341......19059216
%C A198185 .3..56..395...3485...48958....395340....4522496.....41084248.....441157382
%C A198185 .3..70..866..12030..216307...2639341...41084248....559601114....8186901838
%C A198185 .2.171.2346..43774.1155412..19059216..441157382...8186901838..174674654015
%C A198185 .4.256.5663.155664.5522239.135044844.4292509761.115542567852.3432842252818
%H A198185 R. H. Hardin, <a href="/A198185/b198185.txt">Table of n, a(n) for n = 1..179</a>
%e A198185 Some solutions containing all values 0 to 4 for n=6 k=4
%e A198185 ..2..1..1..0....2..1..0..1....0..1..1..2....0..3..0..1....0..1..2..1
%e A198185 ..1..0..2..1....1..0..3..2....1..2..0..1....3..0..3..2....3..0..3..0
%e A198185 ..0..4..0..1....0..4..0..1....1..0..4..0....0..4..0..1....0..4..0..3
%e A198185 ..3..0..1..2....3..0..3..1....2..1..0..3....3..0..3..0....1..0..4..0
%e A198185 ..0..1..1..2....0..3..0..2....2..1..1..0....0..1..1..2....2..3..0..3
%e A198185 ..1..2..0..1....1..2..1..1....1..0..2..1....1..2..0..1....1..0..3..0
%Y A198185 Column 1 is A017817(n+3)
%K A198185 nonn,tabl
%O A198185 1,5
%A A198185 _R. H. Hardin_ Oct 21 2011