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A233073 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.

%I A233073 #6 Jul 23 2025 07:51:24
%S A233073 1,2,2,5,9,5,14,50,50,14,41,289,582,289,41,122,1682,6854,6854,1682,
%T A233073 122,365,9801,80811,164495,80811,9801,365,1094,57122,952869,3957778,
%U A233073 3957778,952869,57122,1094,3281,332929,11235652,95264272,194998895,95264272
%N A233073 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 in row major order.
%C A233073 Table starts
%C A233073 ....1........2...........5.............14................41
%C A233073 ....2........9..........50............289..............1682
%C A233073 ....5.......50.........582...........6854.............80811
%C A233073 ...14......289........6854.........164495...........3957778
%C A233073 ...41.....1682.......80811........3957778.........194998895
%C A233073 ..122.....9801......952869.......95264272........9622519979
%C A233073 ..365....57122....11235652.....2293174089......475027244071
%C A233073 .1094...332929...132484030....55201144642....23452561697310
%C A233073 .3281..1940450..1562171807..1328800293991..1157902539075279
%C A233073 .9842.11309769.18420188169.31986846738550.57168401542703366
%H A233073 R. H. Hardin, <a href="/A233073/b233073.txt">Table of n, a(n) for n = 1..264</a>
%F A233073 Empirical for column k:
%F A233073 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A233073 k=2: a(n) = 7*a(n-1) -7*a(n-2) +a(n-3)
%F A233073 k=3: a(n) = 14*a(n-1) -28*a(n-2) +24*a(n-3) -11*a(n-4) +2*a(n-5) for n>6
%F A233073 k=4: [order 11] for n>12
%F A233073 k=5: [order 21] for n>23
%F A233073 k=6: [order 58] for n>60
%e A233073 Some solutions for n=4 k=4
%e A233073 ..0..0..1..0....0..0..1..1....0..0..0..0....0..1..0..1....0..0..1..1
%e A233073 ..1..1..0..0....0..0..1..0....1..0..2..2....1..0..0..0....0..1..1..1
%e A233073 ..1..1..0..2....0..1..1..1....1..0..2..2....1..0..0..1....0..1..0..0
%e A233073 ..0..1..0..2....1..3..1..3....1..0..0..2....0..0..1..1....0..0..0..2
%Y A233073 Column 1 is A007051(n-1)
%Y A233073 Column 2 is A115599
%K A233073 nonn,tabl
%O A233073 1,2
%A A233073 _R. H. Hardin_, Dec 03 2013