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A233239 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I A233239 #6 Jul 23 2025 07:57:58
%S A233239 1,2,3,6,19,11,23,271,313,48,99,4504,18744,6046,236,452,79201,1212549,
%T A233239 1409129,123352,1248,2136,1419889,79794804,338046654,107709266,
%U A233239 2565169,6896,10313,25622596,5267525102,81477098771,94601758339,8259321811
%N A233239 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%C A233239 Table starts
%C A233239 .......1............2..................6.......................23
%C A233239 .......3...........19................271.....................4504
%C A233239 ......11..........313..............18744..................1212549
%C A233239 ......48.........6046............1409129................338046654
%C A233239 .....236.......123352..........107709266..............94601758339
%C A233239 ....1248......2565169.........8259321811...........26484848685044
%C A233239 ....6896.....53692063.......633724470764.........7415057313896849
%C A233239 ...39168...1126297996.....48630297616989......2076029517168733114
%C A233239 ..226496..23643610702...3731839458899046....581236325493128357679
%C A233239 .1325568.496455294319.286378755661153351.162731637919752077883024
%H A233239 R. H. Hardin, <a href="/A233239/b233239.txt">Table of n, a(n) for n = 1..127</a>
%F A233239 Empirical for column k:
%F A233239 k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
%F A233239 k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)
%F A233239 k=3: a(n) = 93*a(n-1) -1273*a(n-2) +1943*a(n-3) -882*a(n-4) +120*a(n-5)
%F A233239 k=4: a(n) = 311*a(n-1) -8722*a(n-2) +10022*a(n-3) -1645*a(n-4) +35*a(n-5)
%F A233239 Empirical for row n:
%F A233239 n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
%F A233239 n=2: a(n) = 23*a(n-1) -81*a(n-2) -143*a(n-3) +82*a(n-4) +120*a(n-5) for n>6
%F A233239 n=3: [order 9] for n>10
%F A233239 n=4: [order 21] for n>22
%e A233239 Some solutions for n=3 k=4
%e A233239 ..0..1..0..2....0..0..1..2....0..1..0..2....0..0..1..0....0..0..1..2
%e A233239 ..3..3..0..0....4..0..0..3....1..0..0..0....2..0..2..1....2..0..1..5
%e A233239 ..0..3..3..4....3..0..4..2....2..2..0..2....2..1..2..2....1..5..3..5
%Y A233239 Column 1 is A233162(n+1)
%Y A233239 Column 2 is A233107
%Y A233239 Row 1 is A233106
%K A233239 nonn,tabl
%O A233239 1,2
%A A233239 _R. H. Hardin_, Dec 06 2013