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A233026 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

%I A233026 #6 Jul 23 2025 07:47:51
%S A233026 1,3,3,9,15,9,27,81,81,27,81,435,849,435,81,243,2337,8835,8835,2337,
%T A233026 243,729,12555,92067,179999,92067,12555,729,2187,67449,959385,3685017,
%U A233026 3685017,959385,67449,2187,6561,362355,9997413,75489671,149128385
%N A233026 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.
%C A233026 Table starts
%C A233026 .....1........3...........9.............27................81
%C A233026 .....3.......15..........81............435..............2337
%C A233026 .....9.......81.........849...........8835.............92067
%C A233026 ....27......435........8835.........179999...........3685017
%C A233026 ....81.....2337.......92067........3685017.........149128385
%C A233026 ...243....12555......959385.......75489671........6050598339
%C A233026 ...729....67449.....9997413.....1546718177......245698677999
%C A233026 ..2187...362355...104179551....31692006853.....9979662714381
%C A233026 ..6561..1946673..1085618895...649369155341...405380056659145
%C A233026 .19683.10458075.11312857317.13305594622397.16467175046293207
%H A233026 R. H. Hardin, <a href="/A233026/b233026.txt">Table of n, a(n) for n = 1..264</a>
%F A233026 Empirical for column k:
%F A233026 k=1: a(n) = 3*a(n-1)
%F A233026 k=2: a(n) = 5*a(n-1) +2*a(n-2)
%F A233026 k=3: a(n) = 11*a(n-1) -5*a(n-2) -11*a(n-3) +2*a(n-4)
%F A233026 k=4: [order 8]
%F A233026 k=5: [order 20]
%F A233026 k=6: [order 50]
%e A233026 Some solutions for n=4 k=4
%e A233026 ..0..2..2..2....0..0..2..2....0..0..0..2....0..0..0..1....0..0..0..2
%e A233026 ..2..0..0..2....2..2..0..0....0..2..0..0....0..0..0..1....2..2..2..2
%e A233026 ..2..2..0..0....2..2..0..0....0..2..2..2....0..1..1..1....2..2..0..0
%e A233026 ..2..2..2..0....0..0..0..0....2..2..0..0....0..0..0..0....2..2..0..1
%Y A233026 Column 1 is A000244(n-1)
%K A233026 nonn,tabl
%O A233026 1,2
%A A233026 _R. H. Hardin_, Dec 03 2013