A183519
Number of nX2 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
3, 9, 31, 95, 309, 911, 2803, 8673, 26619, 81959, 252477, 777327, 2393627, 7371657, 22698115, 69895583, 215235669, 662786215, 2040959827, 6284869089, 19353386043, 59596135287, 183518286189, 565119695167, 1740209766219, 5358741068409
Offset: 1
Some solutions for 3X2
..1..2....0..2....2..1....2..0....0..2....2..2....1..0....1..0....0..1....1..2
..0..1....1..2....1..2....0..2....1..2....0..0....1..2....1..2....2..1....2..1
..1..2....2..1....0..2....0..0....0..2....1..1....1..0....2..1....1..2....2..0
A183520
Number of n X 3 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
5, 31, 101, 543, 2233, 10003, 47685, 215451, 994397, 4603823, 21240401, 98257363, 454235165, 2100740935, 9717553917, 44943606231, 207898873245, 961691911899, 4448501263357, 20578124472715, 95191234404373, 440340646073843
Offset: 1
Some solutions for 5X3
..2..0..2....2..0..2....2..1..0....0..1..1....2..2..1....1..0..1....2..0..2
..0..2..0....1..2..2....2..2..2....2..1..2....2..2..2....2..1..2....0..2..1
..2..1..2....0..2..0....1..1..2....0..1..0....1..0..1....0..0..0....2..1..0
..2..0..2....0..2..2....2..2..2....2..2..1....2..2..2....2..2..1....2..0..1
..0..1..0....2..1..0....0..1..2....0..1..2....1..2..2....1..2..2....0..0..1
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Configs:= map(t -> convert(t+3^6, base, 3)[1..6],[$0..3^6-1]):
q:= proc(a,b) local A,B;
A:= Configs[a]; B:= Configs[b];
if A[4..6]<> B[1..3] then return 0 fi;
if A[4] <> A[1]+A[5]+B[4] mod 3 and A[4] <> A[2]+B[5] mod 3 then return 0 fi;
if A[5] <> A[2]+A[4]+A[6]+B[5] mod 3 and A[5] <> A[1]+A[3]+B[4]+B[6] mod 3 then return 0 fi;
if A[6] <> A[3]+A[5]+B[6] mod 3 and A[6] <> A[2]+B[5] mod 3 then return 0 fi;
1
end proc:
T:= Matrix(3^6,3^6, q):
u:= Vector[row](3^6,proc(a) if Configs[a][1..3]=[0,0,0] then 1 else 0 fi end proc):
v:= Vector(3^6,proc(a) if Configs[a][4..6]=[0,0,0] then 1 else 0 fi end proc):
V[0]:= v:
for nn from 1 to 30 do V[nn]:= T . V[nn-1] od:
seq(u . V[n],n=1..30); # Robert Israel, Nov 17 2019
A183521
Number of nX4 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
7, 95, 543, 3507, 27609, 201833, 1521573, 11678037, 89238523, 683029435, 5235031077, 40141122349, 307807564417, 2360732530937, 18105826441313, 138867315400205, 1065099011259479, 8169267911756541, 62658120915577663
Offset: 1
Some solutions for 3X4
..2..1..2..1....2..1..0..1....1..1..2..2....2..1..0..0....0..0..2..0
..1..1..0..2....2..2..1..0....0..1..2..0....1..2..2..0....1..0..2..1
..1..2..0..2....1..2..2..1....1..1..2..2....0..2..0..2....2..1..2..2
A183522
Number of nX5 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
13, 309, 2233, 27609, 371691, 4406933, 56562977, 728459961, 9260503697, 118800214951, 1524147275433, 19534446701521, 250583781238959, 3214379129443263, 41229745589418633, 528882044555348133
Offset: 1
Some solutions for 3X5
..2..2..1..0..2....0..2..0..0..0....2..1..1..2..1....0..1..0..0..1
..0..2..0..2..0....1..2..0..1..0....1..0..0..1..2....2..1..0..2..1
..1..1..1..2..2....0..2..0..0..1....0..0..0..0..2....0..1..0..0..1
A183518
Number of n X n 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
1, 9, 101, 3507, 371691, 89738569
Offset: 1
Some solutions for 3X3
..0..0..2....2..2..2....1..1..1....0..0..0....0..1..0....2..0..0....1..2..0
..0..2..0....0..1..0....1..1..0....0..1..0....2..1..2....2..0..1....1..1..1
..0..0..0....0..0..0....1..0..1....1..0..0....1..1..0....0..0..1....0..2..0
A183523
Number of nX6 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
23, 911, 10003, 201833, 4406933, 89738569, 1908431611
Offset: 1
Some solutions for 3X6
..2..1..0..0..2..2....1..1..0..1..0..1....0..2..1..1..0..2....0..2..2..0..1..2
..0..2..0..1..2..1....0..1..1..1..1..0....1..1..2..0..0..2....0..0..0..0..1..1
..2..1..0..0..2..0....1..1..2..1..1..1....1..2..0..2..2..1....0..1..1..0..2..1
A183524
Number of nX7 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
37, 2803, 47685, 1521573, 56562977, 1908431611
Offset: 1
Some solutions for 3X7
..0..2..1..1..2..1..1....2..0..2..1..0..2..2....2..0..2..1..0..2..0
..1..0..1..1..2..1..0....2..0..1..0..0..0..0....2..0..1..0..0..0..2
..0..2..2..2..2..1..1....0..0..2..1..0..1..1....1..2..1..1..0..0..0
A183525
Number of nX8 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.
Original entry on oeis.org
63, 8673, 215451, 11678037, 728459961
Offset: 1
Some solutions for 3X8
..0..2..2..2..1..0..0..1....0..1..1..1..0..1..1..0....0..0..0..1..0..0..1..0
..1..0..1..2..2..1..1..2....2..1..2..0..1..2..0..0....2..0..2..1..1..2..0..2
..0..2..0..0..2..0..1..0....0..1..0..0..2..0..2..2....1..2..1..2..0..1..0..2
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