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A222509 T(n,k)=Number of nXk 0..1 arrays with exactly floor(nXk/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order.

%I A222509 #6 Jul 23 2025 02:41:42
%S A222509 1,0,0,0,0,0,3,4,4,0,4,3,4,11,0,4,10,15,35,8,0,5,32,35,84,87,44,0,20,
%T A222509 44,170,423,497,496,144,0,27,176,441,1753,2066,2862,1335,352,0,48,326,
%U A222509 2192,8489,17674,23678,15420,7552,692,0,63,888,5416,39873,81537,195968,128889
%N A222509 T(n,k)=Number of nXk 0..1 arrays with exactly floor(nXk/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order.
%C A222509 Table starts
%C A222509 .1.....0.......0........3..........4...........4............5...........20
%C A222509 .0.....0.......4........3.........10..........32...........44..........176
%C A222509 .0.....4.......4.......15.........35.........170..........441.........2192
%C A222509 .0....11......35.......84........423........1753.........8489........39873
%C A222509 .0.....8......87......497.......2066.......17674........81537.......800040
%C A222509 .0....44.....496.....2862......23678......195968......1802656.....17117005
%C A222509 .0...144....1335....15420.....128889.....2220730.....19892241....385142640
%C A222509 .0...352....7552....86570....1529195....25587208....473772613...8962277166
%C A222509 .0...692...21382...484976....8569032...297738400...5455705052.212898244002
%C A222509 .0..2488..122942..2751326..102004630..3488244716.132847734428
%C A222509 .0..6476..348597.15597305..577797690.41065342664
%C A222509 .0.17095.2045395.89022483.6918500106
%H A222509 R. H. Hardin, <a href="/A222509/b222509.txt">Table of n, a(n) for n = 1..145</a>
%e A222509 Some solutions for n=3 k=4
%e A222509 ..0..0..0..0....0..0..1..1....0..0..0..0....0..1..1..1....0..1..1..0
%e A222509 ..0..0..0..0....0..0..1..1....0..0..0..0....1..1..1..1....1..1..1..1
%e A222509 ..0..1..0..1....0..0..1..1....0..0..1..1....1..1..1..0....1..1..1..1
%Y A222509 Column 2 is A222284
%Y A222509 Row 1 is A222283
%K A222509 nonn,tabl
%O A222509 1,7
%A A222509 _R. H. Hardin_ Feb 23 2013