|
%I #4 Dec 21 2016 10:40:19
%S 0,1,1,0,4,0,6,33,33,6,6,96,176,96,6,30,255,824,824,255,30,54,610,
%T 3199,5704,3199,610,54,158,1437,11983,37289,37289,11983,1437,158,342,
%U 3292,42296,226118,389786,226118,42296,3292,342,846,7451,143968,1300184
%N T(n,k)=Number of nXk 0..2 arrays with no element unequal 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.........6..........6..........30..........54.........158
%C ...1.....4......33........96........255.........610........1437........3292
%C ...0....33.....176.......824.......3199.......11983.......42296......143968
%C ...6....96.....824......5704......37289......226118.....1300184.....7247300
%C ...6...255....3199.....37289.....389786.....3786373....35086917...313383975
%C ..30...610...11983....226118....3786373....59485548...887774030.12785911872
%C ..54..1437...42296...1300184...35086917...887774030.21336315188
%C .158..3292..143968...7247300..313383975.12785911872
%C .342..7451..476675..39307590.2722202345
%C .846.16662.1543667.208922598
%H R. H. Hardin, <a href="/A279871/b279871.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6)
%F k=2: [order 8] for n>9
%F k=3: [order 12] for n>18
%F k=4: [order 57] for n>64
%e Some solutions for n=4 k=4
%e ..0..1..1..1. .0..1..1..0. .0..1..1..2. .0..1..1..1. .0..0..0..0
%e ..0..1..0..0. .0..1..1..0. .0..1..1..2. .0..1..1..2. .1..1..1..2
%e ..1..1..0..0. .1..1..0..0. .1..1..1..2. .0..0..0..0. .1..1..1..1
%e ..1..1..2..0. .0..0..0..0. .2..2..2..2. .2..2..2..2. .0..0..0..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 21 2016
| 