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%I #4 Nov 16 2013 13:39:57
%S 4,6,9,16,32,25,39,121,156,64,81,406,1024,800,169,168,1225,5778,8464,
%T 4000,441,361,3916,28900,80511,70225,20228,1156,780,12769,155496,
%U 674041,1129755,582169,101808,3025,1681,41180,863041,6257919,15594601,15851094
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to one
%C Table starts
%C .....4........6.........16...........39..............81...............168
%C .....9.......32........121..........406............1225..............3916
%C ....25......156.......1024.........5778...........28900............155496
%C ....64......800.......8464........80511..........674041...........6257919
%C ...169.....4000......70225......1129755........15594601.........245403000
%C ...441....20228.....582169.....15851094.......362293156........9716967198
%C ..1156...101808....4826809....222394359......8404672329......383555570610
%C ..3025...513400...40018276...3120433160....195072388900....15154710590391
%C ..7921..2586980..331786225..43782113196...4526898777801...598600429698510
%C .20736.13039568.2750792704.614302069661.105058031047524.23646568415709520
%H R. H. Hardin, <a href="/A231997/b231997.txt">Table of n, a(n) for n = 1..418</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F k=2: a(n) = 3*a(n-1) +12*a(n-2) -5*a(n-3) -19*a(n-4) +2*a(n-5) +4*a(n-6)
%F k=3: a(n) = 9*a(n-1) -3*a(n-2) -25*a(n-3) +9*a(n-4) +3*a(n-5) -a(n-6)
%F k=4: [order 14]
%F k=5: [order 36]
%F k=6: [order 90] for n>91
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) +3*a(n-5) +3*a(n-6) -2*a(n-8) -a(n-9)
%F n=2: [order 15]
%F n=3: [order 36] for n>38
%e Some solutions for n=4 k=4
%e ..0..0..0..1..1....1..0..0..1..1....0..0..1..0..0....1..0..0..0..0
%e ..0..0..0..0..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
%e ..0..1..0..1..0....0..1..1..0..1....1..0..0..0..0....0..1..0..0..0
%e ..1..0..1..0..0....0..0..0..1..1....1..0..1..1..0....0..0..0..1..0
%e ..0..1..0..0..1....1..0..0..0..0....0..0..0..0..1....1..0..0..0..1
%Y Column 1 is A007598(n+2)
%Y Column 3 is A217022(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 16 2013