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%I #4 Feb 14 2014 07:16:48
%S 2,4,4,7,14,7,12,41,41,12,21,114,184,114,21,37,325,773,773,325,37,65,
%T 943,3373,4826,3373,943,65,114,2731,15038,31651,31651,15038,2731,114,
%U 200,7876,66838,213165,315896,213165,66838,7876,200,351,22702,295601,1428967
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors
%C Table starts
%C ...2.....4.......7........12..........21............37..............65
%C ...4....14......41.......114.........325...........943............2731
%C ...7....41.....184.......773........3373.........15038...........66838
%C ..12...114.....773......4826.......31651........213165.........1428967
%C ..21...325....3373.....31651......315896.......3255233........33328972
%C ..37...943...15038....213165.....3255233......51576880.......810629762
%C ..65..2731...66838...1428967....33328972.....810629762.....19525964230
%C .114..7876..295601...9520138...338653847...12628484789....465620654717
%C .200.22702.1306735..63406826..3440498469..196722783963..11103987320260
%C .351.65489.5781785.422805151.35005538562.3069861742669.265336172863532
%H R. H. Hardin, <a href="/A237859/b237859.txt">Table of n, a(n) for n = 1..337</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) +2*a(n-4) +a(n-5)
%F k=3: [order 11]
%F k=4: [order 21]
%F k=5: [order 46]
%F k=6: [order 98]
%e Some solutions for n=4 k=4
%e ..1..1..0..1..1....1..1..1..1..1....0..0..1..1..1....1..1..1..1..0
%e ..1..1..0..1..1....1..1..0..0..0....0..0..0..1..1....0..0..1..1..0
%e ..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..1..1..1..1....1..1..1..1..1....0..0..1..1..1....1..1..1..1..1
%Y Column 1 is A005251(n+3)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 14 2014
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