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A238323 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.

%I A238323 #6 Jul 23 2025 10:52:11
%S A238323 3,9,9,22,67,22,51,376,376,51,121,1867,4294,1867,121,292,9489,41046,
%T A238323 41046,9489,292,704,50232,405636,721939,405636,50232,704,1691,267174,
%U A238323 4245918,13265123,13265123,4245918,267174,1691,4059,1408341,44773061
%N A238323 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors.
%C A238323 Table starts
%C A238323 ....3.......9.........22............51.............121................292
%C A238323 ....9......67........376..........1867............9489..............50232
%C A238323 ...22.....376.......4294.........41046..........405636............4245918
%C A238323 ...51....1867......41046........721939........13265123..........261676376
%C A238323 ..121....9489.....405636......13265123.......459256128........17315827838
%C A238323 ..292...50232....4245918.....261676376.....17315827838......1266938409578
%C A238323 ..704..267174...44773061....5206684654....658399071392.....93481623913793
%C A238323 .1691.1408341..466364332..102053610873..24577532667851...6747651769489946
%C A238323 .4059.7395987.4831077908.1987295524193.910817281935043.483084194221969236
%H A238323 R. H. Hardin, <a href="/A238323/b238323.txt">Table of n, a(n) for n = 1..144</a>
%F A238323 Empirical for column k:
%F A238323 k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)
%F A238323 k=2: [order 13]
%F A238323 k=3: [order 43]
%e A238323 Some solutions for n=3 k=4
%e A238323 ..2..2..2..2..0....2..2..1..0..0....2..2..2..1..1....2..2..2..1..0
%e A238323 ..2..2..2..0..0....1..1..0..0..0....0..2..2..1..1....2..2..1..1..0
%e A238323 ..2..2..2..0..0....1..1..0..0..0....0..2..2..1..1....0..0..1..1..0
%e A238323 ..2..2..2..1..1....1..1..2..2..1....2..2..2..1..1....0..0..1..1..0
%Y A238323 Column 1 is A202882(n+1)
%K A238323 nonn,tabl
%O A238323 1,1
%A A238323 _R. H. Hardin_, Feb 24 2014