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%I #9 Oct 03 2025 04:08:30
%S 16,43,43,130,174,130,391,689,689,391,1173,2804,3698,2804,1173,3520,
%T 11324,20684,20684,11324,3520,10558,46003,114633,161571,114633,46003,
%U 10558,31672,186672,641743,1252304,1252304,641743,186672,31672,95004
%N T(n,k)=Number of (n+1)X(k+1) binary arrays with no 2X2 subblock commuting with any of its horizontal and vertical 2X2 subblock neighbors.
%C Table starts
%C .....16.......43.......130.........391..........1173............3520
%C .....43......174.......689........2804.........11324...........46003
%C ....130......689......3698.......20684........114633..........641743
%C ....391.....2804.....20684......161571.......1252304.........9823368
%C ...1173....11324....114633.....1252304......13555195.......148669520
%C ...3520....46003....641743.....9823368.....148669520......2287444987
%C ..10558...186672...3588249....76931991....1628541369.....35118814718
%C ..31672...758077..20085335...603313744...17862966996....539993233442
%C ..95004..3077859.112408781..4730797071..195900562382...8301474121906
%C .284980.12497826.629194966.37100667206.2148718629188.127642216451132
%H R. H. Hardin, <a href="/A187729/b187729.txt">Table of n, a(n) for n = 1..199</a>
%e Some solutions for 4X3
%e ..1..1..0....0..1..0....0..1..0....1..1..0....1..1..0....0..1..0....1..1..1
%e ..1..1..1....1..0..0....0..1..0....1..0..0....0..1..0....0..1..1....0..1..1
%e ..1..0..0....1..1..1....1..1..1....1..1..1....0..1..1....1..1..0....0..1..0
%e ..1..0..1....0..1..1....0..0..1....0..0..1....1..1..0....1..0..0....1..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 13 2011