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A197537 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 2,0,1,0,0 for x=0,1,2,3,4.

%I A197537 #7 Jun 02 2025 04:59:03
%S A197537 1,3,3,4,9,4,5,16,16,5,9,33,56,33,9,16,73,216,216,73,16,25,160,868,
%T A197537 1419,868,160,25,39,361,3500,9373,9373,3500,361,39,64,835,14085,62586,
%U A197537 107655,62586,14085,835,64,105,1966,56842,423085,1220630,1220630,423085,56842
%N A197537 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 2,0,1,0,0 for x=0,1,2,3,4.
%C A197537 Every 0 is next to 0 2's, every 1 is next to 1 0'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 A197537 Table starts
%C A197537 ...1....3......4.........5...........9............16..............25
%C A197537 ...3....9.....16........33..........73...........160.............361
%C A197537 ...4...16.....56.......216.........868..........3500...........14085
%C A197537 ...5...33....216......1419........9373.........62586..........423085
%C A197537 ...9...73....868......9373......107655.......1220630........14056707
%C A197537 ..16..160...3500.....62586.....1220630......23325250.......454280983
%C A197537 ..25..361..14085....423085....14056707.....454280983.....14991391782
%C A197537 ..39..835..56842...2879723...162042137....8844380028....493785636151
%C A197537 ..64.1966.229706..19671764..1874230689..172982554332..16343961543732
%C A197537 .105.4703.928664.134643523.21698542215.3386294190736.541269402906501
%H A197537 R. H. Hardin, <a href="/A197537/b197537.txt">Table of n, a(n) for n = 1..180</a>
%e A197537 Some solutions containing all values 0 to 4 for n=6 k=4
%e A197537 ..0..3..0..1....0..3..0..0....0..3..0..0....0..0..0..1....0..3..0..1
%e A197537 ..0..0..3..2....0..0..4..0....3..0..4..0....3..0..3..2....3..0..3..2
%e A197537 ..0..4..0..1....0..0..0..0....0..4..0..0....0..4..0..1....0..4..0..1
%e A197537 ..0..0..3..2....1..3..0..0....3..0..3..0....0..0..3..1....0..0..3..1
%e A197537 ..0..0..0..1....1..0..3..0....0..3..2..1....0..4..0..0....0..0..0..0
%e A197537 ..0..0..0..1....2..1..2..1....0..0..1..2....0..0..3..0....1..1..1..1
%Y A197537 Column 1 is A195971
%K A197537 nonn,tabl
%O A197537 1,2
%A A197537 _R. H. Hardin_ Oct 16 2011