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A241108 T(n,k)=Number of nXk 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.

%I A241108 #6 Jul 23 2025 11:09:36
%S A241108 1,1,1,2,4,2,4,11,11,4,8,36,58,36,8,16,116,294,294,116,16,32,376,1522,
%T A241108 2436,1522,376,32,64,1216,7846,19814,19814,7846,1216,64,128,3936,
%U A241108 40418,162776,259388,162776,40418,3936,128,256,12736,208374,1333934,3374086
%N A241108 T(n,k)=Number of nXk 0..2 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..2 introduced in row major order.
%C A241108 Table starts
%C A241108 ...1.....1.......2.........4...........8.............16...............32
%C A241108 ...1.....4......11........36.........116............376.............1216
%C A241108 ...2....11......58.......294........1522...........7846............40418
%C A241108 ...4....36.....294......2436.......19814.........162776..........1333934
%C A241108 ...8...116....1522.....19814......259388........3374086.........44030862
%C A241108 ..16...376....7846....162776.....3374086.......70145916.......1454236806
%C A241108 ..32..1216...40418...1333934....44030862.....1454236806......48054344508
%C A241108 ..64..3936..208374..10937316...574246744....30189380016....1586763763374
%C A241108 .128.12736.1074002..89651534..7489718098...626548445696...52415988665902
%C A241108 .256.41216.5535686.734979136.97685897406.13004327687556.1731396543937826
%H A241108 R. H. Hardin, <a href="/A241108/b241108.txt">Table of n, a(n) for n = 1..144</a>
%F A241108 Empirical for column k:
%F A241108 k=1: a(n) = 2*a(n-1) for n>2
%F A241108 k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4
%F A241108 k=3: a(n) = 3*a(n-1) +8*a(n-2) +16*a(n-3)
%F A241108 k=4: [order 10]
%F A241108 k=5: [order 26]
%F A241108 k=6: [order 76]
%e A241108 Some solutions for n=4 k=4
%e A241108 ..0..1..1..2....0..1..1..2....0..1..2..0....0..1..0..2....0..1..2..0
%e A241108 ..2..1..1..0....2..1..1..1....1..2..1..2....1..0..2..1....1..0..0..2
%e A241108 ..1..0..2..1....0..2..1..1....2..1..2..0....2..1..1..0....2..0..0..0
%e A241108 ..0..2..0..2....2..0..2..0....1..2..0..2....0..1..1..2....1..2..0..0
%Y A241108 Column 1 is A000079(n-2)
%Y A241108 Column 2 is A206687
%K A241108 nonn,tabl
%O A241108 1,4
%A A241108 _R. H. Hardin_, Apr 16 2014