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A222378 T(n,k)=Number of nXk 0..3 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..3 order.

%I A222378 #6 Jul 23 2025 02:33:10
%S A222378 1,1,1,1,1,1,4,5,5,4,5,18,9,18,5,14,63,118,118,63,14,17,234,498,1391,
%T A222378 498,234,17,75,1163,8111,20340,20340,8111,1163,75,95,4953,37107,
%U A222378 342953,271141,342953,37107,4953,95,411,24021,676485,6221698,16985929,16985929
%N A222378 T(n,k)=Number of nXk 0..3 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..3 order.
%C A222378 Table starts
%C A222378 ....1......1........1..........4...........5..........14..........17
%C A222378 ....1......1........5.........18..........63.........234........1163
%C A222378 ....1......5........9........118.........498........8111.......37107
%C A222378 ....4.....18......118.......1391.......20340......342953.....6221698
%C A222378 ....5.....63......498......20340......271141....16985929...286125939
%C A222378 ...14....234.....8111.....342953....16985929...963154789.61522684225
%C A222378 ...17...1163....37107....6221698...286125939.61522684225
%C A222378 ...75...4953...676485..113556454.20743320247
%C A222378 ...95..24021..3140167.2103238076
%C A222378 ..411.109395.58995438
%C A222378 ..519.536457
%C A222378 .2522
%H A222378 R. H. Hardin, <a href="/A222378/b222378.txt">Table of n, a(n) for n = 1..84</a>
%e A222378 Some solutions for n=4 k=4
%e A222378 ..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..2..2
%e A222378 ..0..0..0..0....0..0..0..0....1..1..0..0....0..2..1..1....1..1..1..2
%e A222378 ..0..0..1..0....0..0..0..0....2..0..0..0....3..1..1..1....1..1..1..1
%e A222378 ..2..1..0..0....1..0..2..2....0..0..0..0....1..1..1..1....1..1..1..1
%K A222378 nonn,tabl
%O A222378 1,7
%A A222378 _R. H. Hardin_ Feb 17 2013