A281936 - OEIS

%I #4 Feb 02 2017 08:25:14

%S 0,0,0,0,0,0,0,1,1,0,0,6,20,6,0,0,33,312,312,33,0,0,166,3573,6304,

%T 3573,166,0,0,792,31410,105766,105766,31410,792,0,0,3654,252630,

%U 1488168,2714834,1488168,252630,3654,0,0,16455,1925590,19173138,60084175

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than four 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.....0........0...........0.............0................0..................0

%C .0.....0........1...........6............33..............166................792

%C .0.....1.......20.........312..........3573............31410.............252630

%C .0.....6......312........6304........105766..........1488168...........19173138

%C .0....33.....3573......105766.......2714834.........60084175.........1216849775

%C .0...166....31410.....1488168......60084175.......2098456730........66997966477

%C .0...792...252630....19173138....1216849775......66997966477......3373640120486

%C .0..3654..1925590...233189094...23300375254....2020027689730....160302681247552

%C .0.16455.14065552..2717934337..428250392864...58434162686355...7305243645203574

%C .0.72774.99735307.30694746766.7629943002132.1637903530180186.322502538593946476

%H R. H. Hardin, <a href="/A281936/b281936.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 6*a(n-1) -3*a(n-2) -14*a(n-3) -21*a(n-4) -12*a(n-5) -4*a(n-6)

%F k=3: [order 21] for n>26

%F k=4: [order 69] for n>74

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Feb 02 2017