|
%I #4 Jan 29 2017 12:40:36
%S 0,0,0,2,4,0,2,14,10,0,5,40,47,20,0,8,110,152,90,38,0,15,280,609,560,
%T 201,68,0,26,698,2138,2808,1872,374,120,0,46,1696,7466,13968,12191,
%U 5948,672,208,0,80,4052,25798,68362,85844,49986,18358,1172,358,0,139,9564,87397
%N T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal 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...........26.............46
%C .0...4...14.....40......110.......280.........698.........1696...........4052
%C .0..10...47....152......609......2138........7466........25798..........87397
%C .0..20...90....560.....2808.....13968.......68362.......323280........1529974
%C .0..38..201...1872....12191.....85844......589990......3845590.......25703392
%C .0..68..374...5948....49986....502276.....4845178.....43943360......414035752
%C .0.120..672..18358...201450...2848436....38998648....491290688.....6531040026
%C .0.208.1172..55048...795220..15817652...306847534...5380228500...100838834642
%C .0.358.2015.162120..3098932..86332266..2376142873..58064622712..1533079336619
%C .0.612.3442.471340.11944444.465260812.18172170592.619082149716.23019093115418
%H R. H. Hardin, <a href="/A281765/b281765.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
%F k=3: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>11
%F k=4: [order 29] for n>32
%F k=5: [order 48] for n>57
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F n=2: [order 9]
%F n=3: [order 40] for n>41
%e Some solutions for n=4 k=4
%e ..0..0..0..0. .0..0..1..1. .0..0..1..0. .0..1..0..0. .0..1..1..0
%e ..0..0..1..1. .0..1..1..1. .0..1..0..1. .1..0..1..1. .0..0..1..1
%e ..1..1..1..1. .0..0..1..1. .1..1..1..0. .0..1..1..1. .0..0..1..1
%e ..1..1..0..1. .0..1..1..1. .1..1..0..0. .1..0..1..1. .0..1..1..1
%Y Column 2 is A279262.
%Y Row 1 is A006367(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Jan 29 2017
| 