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 A279494 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 two elements, and with new values introduced in order 0 sequentially upwards. 7

%I #4 Dec 13 2016 12:22:14

%S 0,1,1,0,0,0,3,5,5,3,3,18,38,18,3,9,68,254,254,68,9,15,235,1433,2684,

%T 1433,235,15,31,801,8330,26157,26157,8330,801,31,57,2678,46095,246237,

%U 425588,246237,46095,2678,57,108,8777,250440,2241332,6559816,6559816

%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 two elements, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ...0.....1.......0..........3............3..............9...............15

%C ...1.....0.......5.........18...........68............235..............801

%C ...0.....5......38........254.........1433...........8330............46095

%C ...3....18.....254.......2684........26157.........246237..........2241332

%C ...3....68....1433......26157.......425588........6559816.........98128162

%C ...9...235....8330.....246237......6559816......166229033.......4065077852

%C ..15...801...46095....2241332.....98128162.....4065077852.....162346342126

%C ..31..2678..250440...19885341...1427793365....96674459373....6294925767121

%C ..57..8777.1332366..172968364..20331614084..2247110811000..238434528280477

%C .108.28343.6989712.1481176019.284582186755.51300573165630.8863487201716422

%H R. H. Hardin, <a href="/A279494/b279494.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

%F k=2: [order 16]

%F k=3: [order 54] for n>55

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A105423(n-2).

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_, Dec 13 2016

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