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A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

%I A240893 #6 Jul 23 2025 11:08:25
%S A240893 1,1,1,2,4,2,4,11,11,4,8,36,57,36,8,16,116,289,289,116,16,32,376,1485,
%T A240893 2362,1485,376,32,64,1216,7609,19065,19065,7609,1216,64,128,3936,
%U A240893 38981,154858,245268,154858,38981,3936,128,256,12736,199761,1255585,3146755
%N A240893 T(n,k)=Number of nXk 0..2 arrays with no element equal to a different number of vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.
%C A240893 Table starts
%C A240893 ...1.....1.......2.........4...........8.............16...............32
%C A240893 ...1.....4......11........36.........116............376.............1216
%C A240893 ...2....11......57.......289........1485...........7609............38981
%C A240893 ...4....36.....289......2362.......19065.........154858..........1255585
%C A240893 ...8...116....1485.....19065......245268........3146755.........40424861
%C A240893 ..16...376....7609....154858.....3146755.......64074526.......1302610899
%C A240893 ..32..1216...38981...1255585....40424861.....1302610899......41971040844
%C A240893 ..64..3936..199761..10186158...519218802....26501432610....1352138182759
%C A240893 .128.12736.1023597..82615013..6669141957...539075345618...43565815810587
%C A240893 .256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757
%H A240893 R. H. Hardin, <a href="/A240893/b240893.txt">Table of n, a(n) for n = 1..180</a>
%F A240893 Empirical for column k:
%F A240893 k=1: a(n) = 2*a(n-1) for n>2
%F A240893 k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4
%F A240893 k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)
%F A240893 k=4: [order 16]
%F A240893 k=5: [order 48]
%e A240893 Some solutions for n=4 k=4
%e A240893 ..0..1..2..1....0..1..2..0....0..1..1..0....0..1..2..1....0..1..2..0
%e A240893 ..1..2..1..0....2..0..0..1....2..1..1..2....2..0..1..2....1..2..0..2
%e A240893 ..2..1..0..2....1..0..0..2....1..0..0..1....1..2..0..1....0..0..2..1
%e A240893 ..1..2..1..0....2..1..2..0....2..0..0..2....0..1..2..0....0..0..1..2
%Y A240893 Column 1 is A000079(n-2)
%Y A240893 Column 2 is A206687
%K A240893 nonn,tabl
%O A240893 1,4
%A A240893 _R. H. Hardin_, Apr 14 2014