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A231663 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.

%I A231663 #6 Jul 23 2025 06:37:22
%S A231663 3,3,3,9,15,9,22,93,93,22,51,458,1197,458,51,121,2163,13434,13434,
%T A231663 2163,121,292,10789,144465,345519,144465,10789,292,704,53813,1607589,
%U A231663 8300390,8300390,1607589,53813,704,1691,265397,17962078,206363144,434469343
%N A231663 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.
%C A231663 Table starts
%C A231663 ....3.......3..........9............22...............51.................121
%C A231663 ....3......15.........93...........458.............2163...............10789
%C A231663 ....9......93.......1197.........13434...........144465.............1607589
%C A231663 ...22.....458......13434........345519..........8300390...........206363144
%C A231663 ...51....2163.....144465.......8300390........434469343.........23632808750
%C A231663 ..121...10789....1607589.....206363144......23632808750.......2825994465190
%C A231663 ..292...53813...17962078....5175246459....1304771142134.....344368908016123
%C A231663 ..704..265397..199451319..128866716238...71426776678405...41555342706134920
%C A231663 .1691.1311447.2215334132.3207643017150.3902799543486962.5000894272327355414
%H A231663 R. H. Hardin, <a href="/A231663/b231663.txt">Table of n, a(n) for n = 1..161</a>
%F A231663 Empirical for column k:
%F A231663 k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6
%F A231663 k=2: [order 15]
%F A231663 k=3: [order 57]
%e A231663 Some solutions for n=3 k=4
%e A231663 ..0..0..0..2....2..1..0..0....0..0..1..1....0..0..1..0....1..1..0..2
%e A231663 ..0..2..0..0....1..1..0..0....0..0..1..0....0..0..0..0....1..0..0..1
%e A231663 ..2..2..0..2....2..2..0..2....1..0..0..0....0..0..1..0....2..0..1..1
%Y A231663 Column 1 is A202882 for n>1
%K A231663 nonn,tabl
%O A231663 1,1
%A A231663 _R. H. Hardin_, Nov 12 2013