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%I #4 Dec 07 2016 08:16:16
%S 0,1,1,0,0,0,3,0,0,3,3,8,16,8,3,9,24,117,117,24,9,15,88,483,864,483,
%T 88,15,31,284,2001,5628,5628,2001,284,31,57,772,7709,34764,57248,
%U 34764,7709,772,57,108,2000,28139,203226,557163,557163,203226,28139,2000,108,199
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its king-move 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......0........8.........24...........88............284
%C ...0....0.....16......117........483.........2001...........7709
%C ...3....8....117......864.......5628........34764.........203226
%C ...3...24....483.....5628......57248.......557163........5159514
%C ...9...88...2001....34764.....557163......8426362......121098448
%C ..15..284...7709...203226....5159514....121098448.....2708250146
%C ..31..772..28139..1143396...45915548...1686053298....58954576326
%C ..57.2000..99519..6219491..396958758..22825771952..1248383818884
%C .108.5008.343156.33013384.3354431037.302051174586.25842455526113
%H R. H. Hardin, <a href="/A279168/b279168.txt">Table of n, a(n) for n = 1..161</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 11]
%F k=3: [order 33] for n>36
%F k=4: [order 84] for n>88
%e Some solutions for n=4 k=4
%e ..0..1..1..1. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e ..1..0..0..0. .1..1..0..1. .0..1..0..0. .1..0..0..1. .0..1..1..1
%e ..0..0..1..0. .0..0..1..1. .0..1..1..0. .1..0..1..1. .0..1..0..0
%e ..1..0..1..1. .1..0..1..0. .1..0..1..0. .1..0..0..0. .1..0..1..1
%Y Column 1 is A105423(n-2).
%K nonn,tabl
%O 1,7
%A _R. H. Hardin_, Dec 07 2016