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A279134 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards. 7

%I

%S 0,1,1,0,0,0,3,9,9,3,3,34,66,34,3,9,87,256,256,87,9,15,194,820,1324,

%T 820,194,15,31,400,2551,6396,6396,2551,400,31,57,790,7491,30074,47452,

%U 30074,7491,790,57,108,1511,21131,129264,316516,316516,129264,21131,1511,108

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical 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.............31

%C ...1....0......9......34........87.........194..........400............790

%C ...0....9.....66.....256.......820........2551.........7491..........21131

%C ...3...34....256....1324......6396.......30074.......129264.........535814

%C ...3...87....820....6396.....47452......316516......2017028.......12376570

%C ...9..194...2551...30074....316516.....3125600.....29410145......266502710

%C ..15..400...7491..129264...2017028....29410145....409061044.....5488392521

%C ..31..790..21131..535814..12376570...266502710...5488392521...109117856920

%C ..57.1511..57971.2150797..73672888..2346800921..71618045798..2111166039927

%C .108.2830.155551.8418336.428568648.20197483932.913912909445.39962431131266

%H R. H. Hardin, <a href="/A279134/b279134.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 8] for n>9

%F k=3: [order 11] for n>17

%F k=4: [order 43] for n>50

%F k=5: [order 88] for n>108

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_, Dec 06 2016

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Last modified January 21 19:21 EST 2022. Contains 350480 sequences. (Running on oeis4.)