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%I #4 May 18 2018 08:15:06
%S 1,2,2,4,8,4,8,21,21,8,16,49,27,49,16,32,120,67,67,120,32,64,293,139,
%T 172,139,293,64,128,719,303,443,443,303,719,128,256,1774,685,1094,
%U 1581,1094,685,1774,256,512,4389,1511,2710,5060,5060,2710,1511,4389,512,1024,10893
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 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....8...21....49....120.....293......719......1774.......4389.......10893
%C ...4...21...27....67....139.....303......685......1511.......3316........7349
%C ...8...49...67...172....443....1094.....2710......6861......17205.......43090
%C ..16..120..139...443...1581....5060....15349.....50030.....160513......515542
%C ..32..293..303..1094...5060...23872...100581....453229....2074725.....9305892
%C ..64..719..685..2710..15349..100581...540901...3257711...19908669...116435693
%C .128.1774.1511..6861..50030..453229..3257711..26814986..224727491..1800071431
%C .256.4389.3316.17205.160513.2074725.19908669.224727491.2642187354.28890049643
%H R. H. Hardin, <a href="/A304775/b304775.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=3: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) for n>8
%F k=4: [order 10] for n>13
%F k=5: [order 25] for n>28
%F k=6: [order 46] for n>50
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..1..1..0. .0..0..0..1
%e ..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
%e ..0..0..1..0. .1..1..1..1. .1..0..0..1. .1..0..0..1. .0..1..1..1
%e ..0..0..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..0
%e ..1..0..0..0. .1..1..1..0. .1..1..1..0. .1..1..1..1. .0..1..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303721.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 18 2018
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