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A233147 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

%I A233147 #6 Jul 23 2025 07:55:20
%S A233147 1,2,2,6,16,6,23,225,225,23,99,3727,13259,3727,99,452,65120,845917,
%T A233147 845917,65120,452,2136,1158334,54777233,198313130,54777233,1158334,
%U A233147 2136,10313,20726079,3556749764,46648134615,46648134615,3556749764,20726079
%N A233147 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
%C A233147 Table starts
%C A233147 ......1............2.................6......................23
%C A233147 ......2...........16...............225....................3727
%C A233147 ......6..........225.............13259..................845917
%C A233147 .....23.........3727............845917...............198313130
%C A233147 .....99........65120..........54777233.............46648134615
%C A233147 ....452......1158334........3556749764..........10976545771938
%C A233147 ...2136.....20726079......231058112982........2582927810338210
%C A233147 ..10313....371568349....15011638934832......607799571521107132
%C A233147 ..50469...6665506622...975308641633714...143023917159921251486
%C A233147 .249062.119595908140.63366149608139911.33655571006177475521033
%H A233147 R. H. Hardin, <a href="/A233147/b233147.txt">Table of n, a(n) for n = 1..144</a>
%F A233147 Empirical for column k:
%F A233147 k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
%F A233147 k=2: a(n) = 25*a(n-1) -134*a(n-2) +134*a(n-3) -25*a(n-4) +a(n-5)
%F A233147 k=3: [order 10] for n>11
%F A233147 k=4: [order 27] for n>28
%e A233147 Some solutions for n=3 k=4
%e A233147 ..0..0..0..1....0..0..0..0....0..0..0..1....0..0..1..1....0..0..0..1
%e A233147 ..1..2..2..2....1..2..2..4....1..0..2..5....2..0..1..5....0..0..2..2
%e A233147 ..2..1..2..4....5..5..2..4....3..4..5..5....1..2..2..2....3..1..0..2
%Y A233147 Column 1 is A233106
%K A233147 nonn,tabl
%O A233147 1,2
%A A233147 _R. H. Hardin_, Dec 04 2013