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A231700 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.

%I A231700 #6 Jul 23 2025 06:38:10
%S A231700 4,4,4,16,28,16,50,272,272,50,144,1998,5972,1998,144,422,13260,115583,
%T A231700 115583,13260,422,1268,94996,2049855,6074096,2049855,94996,1268,3823,
%U A231700 691229,37872601,286808607,286808607,37872601,691229,3823,11472,4926082
%N A231700 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.
%C A231700 Table starts
%C A231700 .....4.........4............16................50....................144
%C A231700 .....4........28...........272..............1998..................13260
%C A231700 ....16.......272..........5972............115583................2049855
%C A231700 ....50......1998........115583...........6074096..............286808607
%C A231700 ...144.....13260.......2049855.........286808607............34764511754
%C A231700 ...422.....94996......37872601.......14007173906..........4333974317355
%C A231700 ..1268....691229.....711067486......696904625544........556835183317668
%C A231700 ..3823...4926082...13223846355....34390368202345......71067313709831125
%C A231700 .11472..35082734..245394073602..1693611631652448....9020067185976407959
%C A231700 .34350.251198534.4563802124823.83546478885400765.1146622410485781036080
%H A231700 R. H. Hardin, <a href="/A231700/b231700.txt">Table of n, a(n) for n = 1..112</a>
%F A231700 Empirical for column k:
%F A231700 k=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8
%F A231700 k=2: [order 22]
%e A231700 Some solutions for n=3 k=4
%e A231700 ..1..0..0..3....2..1..1..2....0..0..0..0....0..3..0..2....0..0..0..0
%e A231700 ..0..0..3..0....0..0..0..3....3..0..0..3....0..0..0..0....0..0..0..3
%e A231700 ..1..3..0..0....0..0..0..2....0..0..0..1....2..0..0..1....2..0..1..3
%Y A231700 Column 1 is A203094 for n>1
%K A231700 nonn,tabl
%O A231700 1,1
%A A231700 _R. H. Hardin_, Nov 12 2013