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%I #7 Apr 20 2021 15:21:25
%S 0,24,24,40,104,40,144,472,472,144,344,1664,1840,1664,344,1000,6848,
%T 10496,10496,6848,1000,2688,27272,46960,59720,46960,27272,2688,7528,
%U 108128,241320,400192,400192,241320,108128,7528,20648,431656,1152312
%N T(n,k) = Number of (n+1) X (k+1) binary arrays with every 2 X 2 subblock trace equal to exactly one or two horizontal and vertical neighbor 2 X 2 subblock traces.
%C Table starts
%C .....0......24........40........144..........344..........1000...........2688
%C ....24.....104.......472.......1664.........6848.........27272.........108128
%C ....40.....472......1840......10496........46960........241320........1152312
%C ...144....1664.....10496......59720.......400192.......2504264.......16124472
%C ...344....6848.....46960.....400192......3026432......25314744......199197496
%C ..1000...27272....241320....2504264.....25314744.....264604776.....2731872328
%C ..2688..108128...1152312...16124472....199197496....2731872328....35582947920
%C ..7528..431656...5769904..102475864...1627815216...28477050608...475637108896
%C .20648.1719312..28108104..654285152..12959411184..295182600552..6259259510232
%C .57040.6845968.138858120.4168475512.105094646680.3063267862112.83202139545720
%H R. H. Hardin, <a href="/A186939/b186939.txt">Table of n, a(n) for n = 1..180</a>
%e Some solutions for 5 X 4
%e ..1..1..1..0....0..1..0..1....1..1..1..0....0..0..1..1....0..0..0..1
%e ..1..1..1..1....1..1..0..0....0..1..1..0....0..1..1..0....0..0..0..0
%e ..1..0..0..0....0..1..1..0....0..0..0..0....0..1..1..0....1..1..1..0
%e ..1..0..0..0....0..1..1..1....1..0..0..0....1..1..1..0....1..0..1..1
%e ..0..0..1..1....1..1..0..1....0..0..1..1....0..1..1..0....1..0..1..1
%Y Column 1 is A185742.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Mar 01 2011