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A231586 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.

%I A231586 #6 Jul 23 2025 06:35:37
%S A231586 4,4,4,16,28,16,50,124,124,50,144,602,2352,602,144,422,2776,32650,
%T A231586 32650,2776,422,1268,12922,381076,1245468,381076,12922,1268,3823,
%U A231586 60720,5618444,38768838,38768838,5618444,60720,3823,11472,286047,82479418,1453028265
%N A231586 T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.
%C A231586 Table starts
%C A231586 .....4.......4...........16...............50................144
%C A231586 .....4......28..........124..............602...............2776
%C A231586 ....16.....124.........2352............32650.............381076
%C A231586 ....50.....602........32650..........1245468...........38768838
%C A231586 ...144....2776.......381076.........38768838.........2912579313
%C A231586 ...422...12922......5618444.......1453028265.......260228939106
%C A231586 ..1268...60720.....82479418......57099276134.....24813120747919
%C A231586 ..3823..286047...1142396851....2144257250786...2275463989704521
%C A231586 .11472.1335296..16061107556...79701582158514.205616812796559119
%C A231586 .34350.6256326.231334122108.3015862229160377
%H A231586 R. H. Hardin, <a href="/A231586/b231586.txt">Table of n, a(n) for n = 1..97</a>
%F A231586 Empirical for column k:
%F A231586 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 A231586 k=2: [order 16]
%F A231586 k=3: [order 72] for n>73
%e A231586 Some solutions for n=3 k=4
%e A231586 ..3..2..1..1....2..0..0..0....1..1..1..3....0..0..1..2....0..3..0..0
%e A231586 ..2..1..1..1....0..0..0..1....1..1..1..2....2..0..0..2....0..0..0..2
%e A231586 ..2..1..1..2....2..0..0..2....1..1..2..2....3..3..0..0....2..0..0..3
%Y A231586 Column 1 is A203094 for n>1
%K A231586 nonn,tabl
%O A231586 1,1
%A A231586 _R. H. Hardin_, Nov 11 2013