A240893 - OEIS

%I #4 Apr 14 2014 06:38:23

%S 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 2362,1485,376,32,64,1216,7609,19065,19065,7609,1216,64,128,3936,

%U 38981,154858,245268,154858,38981,3936,128,256,12736,199761,1255585,3146755

%N 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 Table starts

%C ...1.....1.......2.........4...........8.............16...............32

%C ...1.....4......11........36.........116............376.............1216

%C ...2....11......57.......289........1485...........7609............38981

%C ...4....36.....289......2362.......19065.........154858..........1255585

%C ...8...116....1485.....19065......245268........3146755.........40424861

%C ..16...376....7609....154858.....3146755.......64074526.......1302610899

%C ..32..1216...38981...1255585....40424861.....1302610899......41971040844

%C ..64..3936..199761..10186158...519218802....26501432610....1352138182759

%C .128.12736.1023597..82615013..6669141957...539075345618...43565815810587

%C .256.41216.5245049.670126562.85661208693.10966382557858.1403705064843757

%H R. H. Hardin, <a href="/A240893/b240893.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) for n>2

%F k=2: a(n) = 2*a(n-1) +4*a(n-2) for n>4

%F k=3: a(n) = 3*a(n-1) +8*a(n-2) +14*a(n-3) +4*a(n-4)

%F k=4: [order 16]

%F k=5: [order 48]

%e Some solutions for n=4 k=4

%e ..0..1..2..1....0..1..2..0....0..1..1..0....0..1..2..1....0..1..2..0

%e ..1..2..1..0....2..0..0..1....2..1..1..2....2..0..1..2....1..2..0..2

%e ..2..1..0..2....1..0..0..2....1..0..0..1....1..2..0..1....0..0..2..1

%e ..1..2..1..0....2..1..2..0....2..0..0..2....0..1..2..0....0..0..1..2

%Y Column 1 is A000079(n-2)

%Y Column 2 is A206687

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Apr 14 2014