A183821
1/256 the number of (n+1) X 3 0..3 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
15, 813, 43947, 2377341, 128578815, 6954559893, 376152548283, 20345104031589, 1100412240703119, 59518368554767389, 3219189893127084843, 174117402720326269485, 9417546276713264441151, 509369980225226329837125
Offset: 1
Some solutions with upper left block zero for 5 X 3:
0 0 2 0 0 0 0 0 3 0 0 3 0 0 0 0 0 2 0 0 0
0 0 0 0 0 1 0 0 3 0 0 2 0 0 1 0 0 1 0 0 2
2 0 0 2 0 1 3 0 2 1 0 2 1 0 3 1 0 0 3 0 1
2 2 1 3 2 3 1 3 1 1 3 1 0 3 3 2 1 2 0 3 3
3 2 3 0 0 3 0 0 3 2 0 3 3 2 2 0 0 3 2 2 0
-
Configs:= remove(t -> [t[1],t[4]]=[t[3],t[6]], [seq(convert(4^6+i,base,4)[1..6],i=0..4^6-1)]): nConfigs:= nops(Configs):
Compatible:= proc(i,j) local k;
if Configs[i][4..6] <> Configs[j][1..3] or Configs[i][1..2] =Configs[j][4..5] or Configs[i][2..3] = Configs[j][5..6] then 0 else 1 fi;
end proc:
T:= Matrix(nConfigs,nConfigs,Compatible):
u:= Vector(nConfigs,1):
Tu[0]:= u:
for n from 1 to 30 do Tu[n]:= T . Tu[n-1] od:
seq(u^%T . Tu[n]/256, n=0..30); # Robert Israel, Aug 10 2018
A183820
1/256 the number of (n+1)X(n+1) 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
1, 813, 8538066, 1163575148283, 2051388696859571241
Offset: 1
Some solutions with upper left block zero for 3X3
..0..0..1....0..0..3....0..0..1....0..0..0....0..0..3....0..0..1....0..0..3
..0..0..0....0..0..3....0..0..0....0..0..3....0..0..2....0..0..3....0..0..3
..1..1..3....2..1..1....0..2..1....2..1..0....2..2..2....0..2..1....1..3..1
A183822
1/256 the number of (n+1)X4 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
225, 43947, 8538066, 1661285961, 323115202755, 62851591581012, 12225396762980829, 2378005715920214025, 462553489019014423650, 89972804578123532061801, 17500904466916598194011543
Offset: 1
Some solutions with upper left block zero for 3X4
..0..0..2..1....0..0..2..3....0..0..3..3....0..0..2..0....0..0..3..0
..0..0..0..0....0..0..3..2....0..0..3..0....0..0..1..3....0..0..3..2
..2..3..1..0....3..1..0..1....2..1..2..3....3..3..2..2....0..3..0..3
A183823
1/256 the number of (n+1)X5 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
3375, 2377341, 1661285961, 1163575148283, 814479338538099, 570213177028325955, 399185865558804067443, 279459103250217225077847
Offset: 1
Some solutions with upper left block zero for 3X5
..0..0..2..0..2....0..0..0..0..0....0..0..2..0..0....0..0..0..0..0
..0..0..1..3..0....0..0..2..2..3....0..0..0..2..2....0..0..3..3..2
..0..2..1..2..0....3..0..1..3..3....0..2..2..1..3....2..2..3..3..3
A183824
1/256 the number of (n+1)X6 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
50625, 128578815, 323115202755, 814479338538099, 2051388696859571241, 5167876666358771202411, 13018181193595377140956551
Offset: 1
Some solutions with upper left block zero for 3X6
..0..0..2..2..0..2....0..0..2..2..0..3....0..0..2..2..0..0....0..0..2..0..0..3
..0..0..0..1..0..2....0..0..0..1..0..2....0..0..0..2..0..0....0..0..0..2..0..0
..3..1..0..1..3..1....3..3..0..2..1..0....2..2..0..1..3..3....0..1..3..2..2..1
A183825
1/256 the number of (n+1)X7 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
759375, 6954559893, 62851591581012, 570213177028325955, 5167876666358771202411
Offset: 1
Some solutions with upper left block zero for 3X7
..0..0..2..0..0..0..3....0..0..0..0..1..0..0....0..0..0..0..1..0..2
..0..0..2..2..0..0..0....0..0..3..2..0..0..1....0..0..1..2..0..0..1
..2..0..1..0..1..0..0....2..0..1..0..2..0..2....1..0..3..0..3..0..0
A183826
1/256 the number of (n+1)X8 0..3 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
Original entry on oeis.org
11390625, 376152548283, 12225396762980829, 399185865558804067443, 13018181193595377140956551
Offset: 1
Some solutions with upper left block zero for 3X8
..0..0..1..2..0..0..0..2....0..0..1..2..0..1..0..1....0..0..1..0..0..0..0..2
..0..0..0..3..0..0..2..2....0..0..0..3..0..3..2..2....0..0..0..1..0..0..2..1
..0..2..1..1..0..3..0..3....0..1..1..1..0..2..0..3....0..1..1..2..0..2..0..0
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