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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.

%I A183520 #10 Nov 17 2019 19:19:51
%S A183520 5,31,101,543,2233,10003,47685,215451,994397,4603823,21240401,
%T A183520 98257363,454235165,2100740935,9717553917,44943606231,207898873245,
%U A183520 961691911899,4448501263357,20578124472715,95191234404373,440340646073843
%N 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.
%H A183520 R. H. Hardin, <a href="/A183520/b183520.txt">Table of n, a(n) for n = 1..200</a>
%H A183520 Robert Israel, <a href="/A183520/a183520.txt">Linear recurrence of order 156</a>
%H A183520 Robert Israel, <a href="/A183520/a183520.pdf">Maple-assisted derivation of recurrence</a>
%F A183520 Linear recurrence of order 156: see links. - _Robert Israel_, Nov 17 2019
%e A183520 Some solutions for 5X3
%e A183520 ..2..0..2....2..0..2....2..1..0....0..1..1....2..2..1....1..0..1....2..0..2
%e A183520 ..0..2..0....1..2..2....2..2..2....2..1..2....2..2..2....2..1..2....0..2..1
%e A183520 ..2..1..2....0..2..0....1..1..2....0..1..0....1..0..1....0..0..0....2..1..0
%e A183520 ..2..0..2....0..2..2....2..2..2....2..2..1....2..2..2....2..2..1....2..0..1
%e A183520 ..0..1..0....2..1..0....0..1..2....0..1..2....1..2..2....1..2..2....0..0..1
%p A183520 Configs:= map(t -> convert(t+3^6, base, 3)[1..6],[$0..3^6-1]):
%p A183520 q:= proc(a,b) local A,B;
%p A183520    A:= Configs[a]; B:= Configs[b];
%p A183520    if A[4..6]<> B[1..3] then return 0 fi;
%p A183520    if A[4] <> A[1]+A[5]+B[4] mod 3  and A[4] <> A[2]+B[5] mod 3 then return 0 fi;
%p A183520    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;
%p A183520    if A[6] <> A[3]+A[5]+B[6] mod 3 and A[6] <> A[2]+B[5] mod 3 then return 0 fi;
%p A183520    1
%p A183520 end proc:
%p A183520 T:= Matrix(3^6,3^6, q):
%p A183520 u:= Vector[row](3^6,proc(a) if Configs[a][1..3]=[0,0,0] then 1 else 0 fi end proc):
%p A183520 v:= Vector(3^6,proc(a) if Configs[a][4..6]=[0,0,0] then 1 else 0 fi end proc):
%p A183520 V[0]:= v:
%p A183520 for nn from 1 to 30 do V[nn]:= T . V[nn-1] od:
%p A183520 seq(u . V[n],n=1..30); # _Robert Israel_, Nov 17 2019
%Y A183520 Column 3 of A183526.
%K A183520 nonn
%O A183520 1,1
%A A183520 _R. H. Hardin_, Jan 05 2011