It is well-known, but up to n=9, I verified via running my fast-made mixed integer program containing real and binary variables only - in GMPL, to be published later. I am aware that this had been done by others earlier, just for fun
An excerpt from logs when determining n=9 case:
Undoctored console dump for smaller areas:+35650619: mip = 4.300000000e+01 <= 4.400000000e+01 2.3% (425; 358842)
+35673703: mip = 4.300000000e+01 <= 4.400000000e+01 2.3% (332; 359323)
Warning: numerical instability (dual simplex, phase II)
+35697025: mip = 4.300000000e+01 <= 4.400000000e+01 2.3% (273; 359753)
+35713230: mip = 4.300000000e+01 <= tree is empty 0.0% (0; 363429)
INTEGER OPTIMAL SOLUTION FOUND
Time used: 11618.0 secs
Memory used: 502.7 Mb (527138079 bytes)Model has been successfully processedCode: Select all
x = 9 , y = 9 , rule = B3/S23 obooboobo$ooboboboo$bbbobobbb$ooboboooo$oobobbbbo$bbbooooob$ooobbbbbb$obboboobo$bbooboboo$!
SZUPER
user@:0:~/20200724$
user@errorlevel:0:~/.golly/Downloads/privat/20200724$ for((i=2;i<=8;i++));{ for((j=i;j<=i;j++));{ echo 'param Xmax := '"$i"'; param Ymax := '"$j"';' | glpsol --proxy 6 --cuts -m densest.mod -d /dev/stdin;};} | sed -nre '/^.code/,/^..code/p'
Code: Select all
x = 2 , y = 2 , rule = B3/S23
oo$oo$!
Code: Select all
x = 3 , y = 3 , rule = B3/S23
oob$obo$boo$!
Code: Select all
x = 4 , y = 4 , rule = B3/S23
oobb$obob$bobo$bboo$!
Code: Select all
x = 5 , y = 5 , rule = B3/S23
ooboo$ooboo$bbbbb$ooboo$ooboo$!
Code: Select all
x = 6 , y = 6 , rule = B3/S23
oobboo$obbobo$boboob$oobbbb$bboobo$bboboo$!
Code: Select all
x = 7 , y = 7 , rule = B3/S23
obooboo$oobobob$bbbobbo$ooobooo$obbobbb$boboboo$ooboobo$!
Code: Select all
x = 8 , y = 8 , rule = B3/S23
oobooboo$oobooboo$bbbbbbbb$oobooboo$oobooboo$bbbbbbbb$oobooboo$oobooboo$!
[APPEND#1]
up to 6x6, all rectangles in one pattern:
Code: Select all
x = 21, y = 153, rule = B3/S23
obobobobobobobobobobo6$obobobobobobobobobobo3$2o$2o3$obobobobobobobobo
bobo6$obobobobobobobobobobo3$2o$2o3$obobobobobobobobobobo3$2o$obo$b2o
3$obobobobobobobobobobo6$obobobobobobobobobobo3$2obo$ob2o3$obobobobobo
bobobobobo3$b2o$o2bo$b2o3$obobobobobobobobobobo3$2o$obo$bobo$2b2o3$obo
bobobobobobobobobo6$obobobobobobobobobobo3$2ob2o$2ob2o3$obobobobobobob
obobobo3$2o$o2b2o$b2obo3$obobobobobobobobobobo3$2ob2o$bobo$bobo$2ob2o
3$obobobobobobobobobobo3$2ob2o$2ob2o2$2ob2o$2ob2o3$obobobobobobobobobo
bo6$obobobobobobobobobobo3$b2ob2o$b2ob2o3$obobobobobobobobobobo3$2ob2o
$2obobo$4b2o3$obobobobobobobobobobo3$b2ob2o$obobo$obobo$b2ob2o3$obobob
obobobobobobobo3$2ob2o$bob2o$o$ob2obo$b2ob2o3$obobobobobobobobobobo3$
2o2b2o$o2bobo$bob2o$2o$2b2obo$2bob2o!