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A300208 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%I A300208 #4 Feb 28 2018 14:16:03
%S A300208 1,2,2,4,8,4,8,32,32,8,16,128,248,128,16,32,512,1933,1933,512,32,64,
%T A300208 2048,15070,29561,15070,2048,64,128,8192,117494,451996,451996,117494,
%U A300208 8192,128,256,32768,916061,6912249,13548425,6912249,916061,32768,256,512,131072
%N A300208 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C A300208 Table starts
%C A300208 ...1......2........4...........8.............16...............32
%C A300208 ...2......8.......32.........128............512.............2048
%C A300208 ...4.....32......248........1933..........15070...........117494
%C A300208 ...8....128.....1933.......29561.........451996..........6912249
%C A300208 ..16....512....15070......451996.......13548425........406228452
%C A300208 ..32...2048...117494.....6912249......406228452......23883950854
%C A300208 ..64...8192...916061...105708560....12180207076....1404241937017
%C A300208 .128..32768..7142233..1616600364...365209429387...82562348427139
%C A300208 .256.131072.55685704.24722667407.10950385677546.4854250928660105
%H A300208 R. H. Hardin, <a href="/A300208/b300208.txt">Table of n, a(n) for n = 1..220</a>
%F A300208 Empirical for column k:
%F A300208 k=1: a(n) = 2*a(n-1)
%F A300208 k=2: a(n) = 4*a(n-1)
%F A300208 k=3: a(n) = 8*a(n-1) -2*a(n-2) +5*a(n-3) -13*a(n-4) -6*a(n-5)
%F A300208 k=4: [order 15]
%F A300208 k=5: [order 38]
%e A300208 Some solutions for n=5 k=4
%e A300208 ..0..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..1
%e A300208 ..1..0..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..1..0
%e A300208 ..0..1..1..0. .0..0..1..1. .1..0..1..1. .0..0..0..0. .0..0..1..0
%e A300208 ..1..1..1..0. .0..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..1
%e A300208 ..0..1..0..0. .0..1..1..1. .0..1..1..1. .1..1..0..1. .1..0..1..0
%Y A300208 Column 1 is A000079(n-1).
%Y A300208 Column 2 is A004171(n-1).
%K A300208 nonn,tabl
%O A300208 1,2
%A A300208 _R. H. Hardin_, Feb 28 2018