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.

5, 31, 101, 543, 2233, 10003, 47685, 215451, 994397, 4603823, 21240401, 98257363, 454235165, 2100740935, 9717553917, 44943606231, 207898873245, 961691911899, 4448501263357, 20578124472715, 95191234404373, 440340646073843

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Linear recurrence of order 156

Robert Israel, Maple-assisted derivation of recurrence

Formula

Linear recurrence of order 156: see links. - Robert Israel, Nov 17 2019

Example

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

Maple

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

Crossrefs

Column 3 of A183526.

Sequence in context: A211923 A362304 A024399 * A099083 A212523 A096944

Adjacent sequences: A183517 A183518 A183519 * A183521 A183522 A183523

Keyword

nonn

Author

R. H. Hardin, Jan 05 2011

Status

approved