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%I #4 Dec 26 2016 08:00:35
%S 0,0,0,2,4,2,2,8,8,2,8,28,37,28,8,14,80,168,168,80,14,36,252,705,1030,
%T 705,252,36,74,776,2852,5802,5802,2852,776,74,168,2356,11249,31608,
%U 44382,31608,11249,2356,168,358,7200,44120,171100,330254,330254,171100,44120
%N T(n,k)=Number of nXk 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical 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.........8.........14.........36.........74
%C ...0.....4......8.......28........80........252........776.......2356
%C ...2.....8.....37......168.......705.......2852......11249......44120
%C ...2....28....168.....1030......5802......31608.....171100.....916768
%C ...8....80....705.....5802.....44382.....330254....2433834...17647668
%C ..14...252...2852....31608....330254....3348206...33510642..330506508
%C ..36...776..11249...171100...2433834...33510642..454149404.6104734752
%C ..74..2356..44120...916768..17647668..330506508.6104734752
%C .168..7200.172216..4882310.127427398.3241940520
%C .358.21836.669642.25849910.911386034
%H R. H. Hardin, <a href="/A280124/b280124.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=2: a(n) = 2*a(n-1) +7*a(n-2) -24*a(n-4) -32*a(n-5) -16*a(n-6) for n>8
%F k=3: [order 14] for n>19
%F k=4: [order 28] for n>34
%F k=5: [order 86] for n>96
%e Some solutions for n=4 k=4
%e ..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..0
%e ..0..2..2..1. .0..1..1..1. .0..1..1..1. .1..1..0..0. .0..0..0..1
%e ..2..2..2..1. .1..1..1..2. .1..1..1..1. .1..1..0..0. .2..2..1..1
%e ..2..2..1..1. .1..1..2..2. .1..1..0..1. .1..1..0..0. .2..1..1..1
%Y Column 1 is 2*A219754(n+1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Dec 26 2016
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