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A230757 T(n,k)=Number of (n+3)X(k+3) 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

%I A230757 #6 Jul 23 2025 06:00:24
%S A230757 12,192,192,2700,5544,2700,31212,178608,178608,31212,363312,4838400,
%T A230757 13305708,4838400,363312,4120752,129731328,820317888,820317888,
%U A230757 129731328,4120752,46949808,3423037464,51048476748,116879941620,51048476748
%N A230757 T(n,k)=Number of (n+3)X(k+3) 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
%C A230757 Table starts
%C A230757 .......12.........192............2700..............31212................363312
%C A230757 ......192........5544..........178608............4838400.............129731328
%C A230757 .....2700......178608........13305708..........820317888...........51048476748
%C A230757 ....31212.....4838400.......820317888.......116879941620........17027460691212
%C A230757 ...363312...129731328.....51048476748.....17027460691212......5769362600920812
%C A230757 ..4120752..3423037464...3154520054700...2446111719135732...1928867953682733132
%C A230757 .46949808.90231813552.194576103540300.350956390609736652.645610139671314494208
%H A230757 R. H. Hardin, <a href="/A230757/b230757.txt">Table of n, a(n) for n = 1..180</a>
%F A230757 Empirical for column k:
%F A230757 k=1: [order 15]
%F A230757 k=2: [order 36]
%F A230757 T(n,k)=3*A230708(n,k)*A230739(n,k)
%e A230757 Some solutions for n=1 k=4
%e A230757 ..0..0..2..2..0..0..0....0..2..0..0..1..1..2....0..1..0..2..1..0..2
%e A230757 ..1..1..0..0..1..1..2....0..1..2..2..1..0..2....2..1..0..2..1..0..2
%e A230757 ..0..2..0..1..1..0..2....0..1..2..2..1..0..2....0..0..2..2..1..0..2
%e A230757 ..1..2..0..2..2..0..2....0..2..0..0..1..0..2....2..2..1..0..2..0..2
%K A230757 nonn,tabl
%O A230757 1,1
%A A230757 _R. H. Hardin_, Oct 29 2013