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%I #4 Jul 02 2018 09:07:06
%S 1,2,2,4,4,4,8,5,5,8,16,9,14,9,16,32,22,27,27,22,32,64,45,66,93,66,45,
%T 64,128,101,180,287,287,180,101,128,256,218,484,1009,1265,1009,484,
%U 218,256,512,477,1261,3496,5695,5695,3496,1261,477,512,1024,1041,3346,11962
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1...2....4.....8.....16......32.......64........128.........256..........512
%C ...2...4....5.....9.....22......45......101........218.........477.........1041
%C ...4...5...14....27.....66.....180......484.......1261........3346.........8912
%C ...8...9...27....93....287....1009.....3496......11962.......41160.......142076
%C ..16..22...66...287...1265....5695....25312.....112499......501646......2235513
%C ..32..45..180..1009...5695...33380...192752....1116462.....6489620.....37702431
%C ..64.101..484..3496..25312..192752..1459806...11066456....84120192....639206832
%C .128.218.1261.11962.112499.1116462.11066456..110043463..1095070964..10891632449
%C .256.477.3346.41160.501646.6489620.84120192.1095070964.14254922771.185426707377
%H R. H. Hardin, <a href="/A316420/b316420.txt">Table of n, a(n) for n = 1..311</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
%F k=3: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4) -3*a(n-5) -9*a(n-6) -6*a(n-7) for n>10
%F k=4: [order 19] for n>23
%F k=5: [order 43] for n>49
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .0..1..0..0
%e ..0..0..0..0. .1..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
%e ..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .1..0..0..0
%e ..0..0..0..1. .0..0..0..1. .0..1..0..1. .0..0..0..0. .0..0..1..0
%e ..0..1..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..0. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A052962 for n>2.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 02 2018
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