Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Jan 04 2017 06:29:02
%S 0,1,0,0,6,0,6,22,30,0,6,63,208,158,0,30,162,997,1939,846,0,54,381,
%T 4070,15104,17406,4446,0,158,884,15441,100306,214635,149057,22734,0,
%U 342,1995,55149,618883,2272190,2886700,1224092,113310,0,846,4478,189470,3589912
%N T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal 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
%C .0.......6........22..........63..........162..........381..........884
%C .0......30.......208.........997.........4070........15441........55149
%C .0.....158......1939.......15104.......100306.......618883......3589912
%C .0.....846.....17406......214635......2272190.....22475478....208736159
%C .0....4446....149057.....2886700.....48481917....767741328..11437392975
%C .0...22734...1224092....37224679....990070284..25082093017.599110195185
%C .0..113310...9717407...464804972..19550495121.792009247239
%C .0..552654..75078490..5658641517.375972018492
%C .0.2647390.567486429.67497024458
%H R. H. Hardin, <a href="/A280480/b280480.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 15*a(n-1) -87*a(n-2) +245*a(n-3) -348*a(n-4) +240*a(n-5) -64*a(n-6)
%F k=3: [order 9] for n>10
%F k=4: [order 21] for n>22
%F k=5: [order 38] for n>39
%F Empirical for row n:
%F n=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 n=2: [order 8] for n>10
%F n=3: [order 26] for n>32
%e Some solutions for n=4 k=4
%e ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..1. .0..0..1..1
%e ..1..1..0..0. .0..1..1..1. .1..1..0..0. .2..2..1..1. .1..1..0..0
%e ..0..0..1..2. .0..1..1..2. .1..0..2..2. .2..2..2..2. .0..0..0..0
%e ..1..1..2..2. .1..2..2..2. .2..2..1..1. .2..1..1..1. .2..0..0..0
%Y Row 1 is A279865.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 04 2017