|
%I #4 Dec 12 2016 15:20:42
%S 0,0,0,2,2,2,2,6,6,2,5,20,33,20,5,8,66,180,180,66,8,15,210,1024,1722,
%T 1024,210,15,26,658,5228,15484,15484,5228,658,26,46,2036,26670,129914,
%U 223261,129914,26670,2036,46,80,6236,134438,1079792,3086910,3086910
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ..0.....0.......2.........2...........5..............8...............15
%C ..0.....2.......6........20..........66............210..............658
%C ..2.....6......33.......180........1024...........5228............26670
%C ..2....20.....180......1722.......15484.........129914..........1079792
%C ..5....66....1024.....15484......223261........3086910.........41706415
%C ..8...210....5228....129914.....3086910.......69493918.......1529974962
%C .15...658...26670...1079792....41706415.....1529974962......54755104784
%C .26..2036..134438...8845592...555052466....33126514762....1926654903560
%C .46..6236..670407..71540206..7290902341...707716447612...66854006751350
%C .80.18928.3310176.572555634.94741575142.14949807134092.2293311539588776
%H R. H. Hardin, <a href="/A279466/b279466.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) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F k=2: [order 10]
%F k=3: [order 36]
%e Some solutions for n=4 k=4
%e ..0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..0
%e ..1..0..1..0. .0..0..1..0. .1..1..1..1. .0..0..1..1. .1..1..1..1
%e ..1..0..0..1. .1..0..1..1. .0..1..0..0. .1..0..1..0. .0..0..1..0
%e ..1..1..0..0. .0..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1
%Y Column 1 is A006367(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 12 2016
| 