login
T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
5

%I #4 Dec 14 2016 10:25:40

%S 0,1,1,0,0,0,3,15,15,3,6,222,668,222,6,24,2348,21430,21430,2348,24,72,

%T 21302,539596,1585524,539596,21302,72,232,176125,12335295,102868091,

%U 102868091,12335295,176125,232,720,1370378,263171408,6167352480

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ....0........1............0..............3...............6...............24

%C ....1........0...........15............222............2348............21302

%C ....0.......15..........668..........21430..........539596.........12335295

%C ....3......222........21430........1585524.......102868091.......6167352480

%C ....6.....2348.......539596......102868091.....17596660798....2810209481878

%C ...24....21302.....12335295.....6167352480...2810209481878.1203474431523240

%C ...72...176125....263171408...349780411336.427316604639150

%C ..232..1370378...5359546513.19062177795838

%C ..720.10206549.105415261452

%C .2232.73563740

%H R. H. Hardin, <a href="/A279534/b279534.txt">Table of n, a(n) for n = 1..71</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>8

%F k=2: [order 12] for n>13

%F k=3: [order 33] for n>35

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A279300.

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_, Dec 14 2016