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%I #4 Mar 01 2018 07:47:58
%S 1,2,2,4,8,4,8,31,31,8,16,121,179,121,16,32,472,1080,1080,472,32,64,
%T 1841,6585,10363,6585,1841,64,128,7181,40023,100823,100823,40023,7181,
%U 128,256,28010,243312,974646,1588195,974646,243312,28010,256,512,109255,1479656
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1......2.......4.........8..........16............32...............64
%C ...2......8......31.......121.........472..........1841.............7181
%C ...4.....31.....179......1080........6585.........40023...........243312
%C ...8....121....1080.....10363......100823........974646..........9424684
%C ..16....472....6585....100823.....1588195......24735890........385299869
%C ..32...1841...40023....974646....24735890.....618957455......15475106013
%C ..64...7181..243312...9424684...385299869...15475106013.....620657860617
%C .128..28010.1479656..91234133..6015414147..388173584774...24999315059414
%C .256.109255.8997567.882982660.93883095950.9733989458695.1006615871837972
%H R. H. Hardin, <a href="/A300259/b300259.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
%F k=3: [order 11] for n>12
%F k=4: [order 38] for n>39
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..0..1..0. .0..0..1..0. .0..1..0..1. .0..1..1..0
%e ..0..1..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..0..1..0
%e ..1..1..0..1. .1..0..1..1. .1..0..0..1. .1..0..0..0. .1..0..1..1
%e ..0..0..0..1. .1..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0
%e ..1..1..0..1. .0..0..1..1. .1..0..1..0. .1..1..0..1. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A281831.
%Y Column 3 is A299663.
%Y Column 4 is A299664.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 01 2018
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