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A233230 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, 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 A233230 #6 Jul 23 2025 07:57:17
%S A233230 1,2,2,6,14,6,23,174,174,23,99,2541,8231,2541,99,452,39203,420948,
%T A233230 420948,39203,452,2136,616454,21895530,72049266,21895530,616454,2136,
%U A233230 10313,9757236,1142726121,12389989684,12389989684,1142726121,9757236,10313
%N A233230 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, 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 A233230 Table starts
%C A233230 ......1...........2................6.....................23
%C A233230 ......2..........14..............174...................2541
%C A233230 ......6.........174.............8231.................420948
%C A233230 .....23........2541...........420948...............72049266
%C A233230 .....99.......39203.........21895530............12389989684
%C A233230 ....452......616454.......1142726121..........2131764323784
%C A233230 ...2136.....9757236......59679029456........366805442634477
%C A233230 ..10313...154782591....3117164734533......63115455429961173
%C A233230 ..50469..2457231917..162820623245643...10860156414181066717
%C A233230 .249062.39019481264.8504746957840386.1868686679256045815893
%H A233230 R. H. Hardin, <a href="/A233230/b233230.txt">Table of n, a(n) for n = 1..112</a>
%F A233230 Empirical for column k:
%F A233230 k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
%F A233230 k=2: a(n) = 21*a(n-1) -79*a(n-2) -41*a(n-3) +72*a(n-4) +28*a(n-5)
%F A233230 k=3: [order 10]
%F A233230 k=4: [order 23]
%e A233230 Some solutions for n=3 k=4
%e A233230 ..0..1..1..1....0..1..2..1....0..1..1..2....0..1..0..0....0..1..2..1
%e A233230 ..1..0..2..5....3..0..1..1....1..0..2..2....1..0..2..4....0..0..2..2
%e A233230 ..1..0..1..1....3..0..2..5....1..1..1..1....1..2..4..5....0..1..1..0
%Y A233230 Column 1 is A233106
%K A233230 nonn,tabl
%O A233230 1,2
%A A233230 _R. H. Hardin_, Dec 06 2013