A240642 - OEIS

%I #6 Jul 23 2025 11:04:12

%S 1,1,1,2,5,2,5,27,27,5,14,193,462,193,14,41,1391,7993,7993,1391,41,

%T 122,10072,138882,333308,138882,10072,122,365,72941,2413198,13897353,

%U 13897353,2413198,72941,365,1094,528283,41931738,579476701,1390560136

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to one or three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

%C Table starts

%C ....1........1............2................5...................14

%C ....1........5...........27..............193.................1391

%C ....2.......27..........462.............7993...............138882

%C ....5......193.........7993...........333308.............13897353

%C ...14.....1391.......138882.........13897353...........1390560136

%C ...41....10072......2413198........579476701.........139138607313

%C ..122....72941.....41931738......24162243789.......13922129807222

%C ..365...528283....728606311....1007486056500.....1393040370960551

%C .1094..3826157..12660271050...42008844856285...139386826311366370

%C .3281.27711478.219985006177.1751630302786777.13946966455660995272

%H R. H. Hardin, <a href="/A240642/b240642.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3

%F k=2: a(n) = 6*a(n-1) +10*a(n-2) -6*a(n-3) -9*a(n-4) for n>6

%F k=3: a(n) = 14*a(n-1) +54*a(n-2) +82*a(n-3) -14*a(n-4) -54*a(n-5) -81*a(n-6)

%F k=4: [order 14]

%F k=5: [order 31]

%e Some solutions for n=3 k=4

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

%e ..1..0..1..0....1..2..0..1....2..0..3..2....1..2..3..2....1..2..1..2

%e ..0..2..0..1....3..0..3..2....3..1..2..3....3..1..2..3....2..0..2..1

%Y Column 1 is A007051(n-2)

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Apr 09 2014