A281988 - OEIS

%I #4 Feb 04 2017 09:18:15

%S 0,0,0,0,0,0,0,2,2,0,0,16,121,16,0,0,88,1054,1054,88,0,0,432,7053,

%T 10852,7053,432,0,0,2008,41118,89414,89414,41118,2008,0,0,8992,226025,

%U 659508,938730,659508,226025,8992,0,0,39200,1189600,4668914,8777256,8777256

%N T(n,k)=Number of nXk 0..1 arrays with no element unequal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C .0......0........0..........0...........0.............0..............0

%C .0......0........2.........16..........88...........432...........2008

%C .0......2......121.......1054........7053.........41118.........226025

%C .0.....16.....1054......10852.......89414........659508........4668914

%C .0.....88.....7053......89414......938730.......8777256.......77613062

%C .0....432....41118.....659508.....8777256.....104671608.....1170765416

%C .0...2008...226025....4668914....77613062....1170765416....16521306352

%C .0...8992..1189600...31829068...662453196...12655050072...225583845888

%C .0..39200..6090935..212313306..5524744676..133501129836..3008079936046

%C .0.167552.30538028.1390961304.45282954978.1383406166720.39403294497598

%H R. H. Hardin, <a href="/A281988/b281988.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) =

%F k=2: a(n) = 8*a(n-1) -20*a(n-2) +24*a(n-3) -36*a(n-4) +16*a(n-5) -16*a(n-6)

%F k=3: [order 20] for n>23

%F k=4: [order 56] for n>63

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Feb 04 2017