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A231396 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231396 #6 Jul 23 2025 06:27:32
%S A231396 3,7,4,14,8,7,33,38,15,12,78,90,100,20,23,189,363,311,272,31,44,482,
%T A231396 1163,1706,1096,740,52,87,1225,3985,7844,8340,4085,2061,95,172,3238,
%U A231396 14650,35696,55788,41237,15732,5834,180,343,8565,50088,184692,345022,401240
%N A231396 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231396 Table starts
%C A231396 ...3...7.....14......33........78........189........482.......1225.......3238
%C A231396 ...4...8.....38......90.......363.......1163.......3985......14650......50088
%C A231396 ...7..15....100.....311......1706.......7844......35696.....184692.....873979
%C A231396 ..12..20....272....1096......8340......55788.....345022....2502891...16525492
%C A231396 ..23..31....740....4085.....41237.....401240....3407422...34218952..319475231
%C A231396 ..44..52...2061...15732....217846....3002376...35510853..491895476.6459555901
%C A231396 ..87..95...5834...62039...1158551...22654165..374180527.7170248270
%C A231396 .172.180..16521..245850...6261166..172363558.3979476204
%C A231396 .343.351..46969..980361..34110556.1318257485
%C A231396 .684.692.133864.3915982.186830745
%H A231396 R. H. Hardin, <a href="/A231396/b231396.txt">Table of n, a(n) for n = 1..111</a>
%F A231396 Empirical for column k:
%F A231396 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F A231396 k=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) for n>5
%F A231396 k=3: [order 18]
%F A231396 k=4: [order 28] for n>31
%F A231396 Empirical for row n:
%F A231396 n=1: a(n) = 4*a(n-1) +a(n-2) -16*a(n-3) +4*a(n-4) +24*a(n-5) -16*a(n-6)
%F A231396 n=2: [order 21]
%F A231396 n=3: [order 83]
%e A231396 Some solutions for n=4 k=4
%e A231396 ..0..0..0..0..0....0..0..1..1..1....0..0..1..1..1....0..1..1..1..1
%e A231396 ..1..1..0..0..0....1..1..0..0..0....0..1..0..1..1....1..0..0..0..0
%e A231396 ..1..1..1..0..0....1..1..1..0..0....1..0..1..0..0....1..1..0..0..0
%e A231396 ..1..1..0..0..0....1..1..0..0..0....1..1..0..0..0....1..1..1..2..2
%e A231396 ..1..1..1..0..0....0..0..0..0..0....1..1..1..1..1....1..1..2..2..2
%Y A231396 Column 1 is A023105(n+2)
%K A231396 nonn,tabl
%O A231396 1,1
%A A231396 _R. H. Hardin_, Nov 08 2013