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A231977 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

%I A231977 #6 Jul 23 2025 06:46:23
%S A231977 9,16,16,36,56,36,81,169,169,81,169,550,841,550,169,361,1764,4489,
%T A231977 4489,1764,361,784,5680,24964,43983,24964,5680,784,1681,18225,136900,
%U A231977 417316,417316,136900,18225,1681,3600,58596,741321,3844551,6507601,3844551
%N A231977 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.
%C A231977 Table starts
%C A231977 ....9.....16........36..........81...........169..............361
%C A231977 ...16.....56.......169.........550..........1764.............5680
%C A231977 ...36....169.......841........4489.........24964...........136900
%C A231977 ...81....550......4489.......43983........417316..........3844551
%C A231977 ..169...1764.....24964......417316.......6507601........100540729
%C A231977 ..361...5680....136900.....3844551.....100540729.......2641967397
%C A231977 ..784..18225....741321....35366809....1557328369......69043343121
%C A231977 .1681..58596...4024036...328433132...24225988609....1809552010404
%C A231977 .3600.188356..21911761..3052452001..376708702756...47496507516441
%C A231977 .7744.605458.119268241.28290095075.5849616285604.1245162776547248
%H A231977 R. H. Hardin, <a href="/A231977/b231977.txt">Table of n, a(n) for n = 1..475</a>
%F A231977 Empirical for column k:
%F A231977 k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
%F A231977 k=2: a(n) = 3*a(n-1) +2*a(n-3) +4*a(n-4) -10*a(n-5) -2*a(n-6) -a(n-8) +a(n-9)
%F A231977 k=3: [order 21]
%F A231977 k=4: [order 49]
%e A231977 Some solutions for n=2 k=4
%e A231977 ..0..1..1..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..1..0
%e A231977 ..0..0..0..0..0....1..0..0..0..0....0..1..0..0..0....0..0..0..0..0
%e A231977 ..1..0..0..1..0....0..0..0..1..0....0..1..0..0..0....1..0..0..1..1
%Y A231977 Column 1 is A207170 for n>1
%K A231977 nonn,tabl
%O A231977 1,1
%A A231977 _R. H. Hardin_, Nov 16 2013