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%I #4 Jan 12 2018 09:33:00
%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,19,19,23,5,8,49,21,30,21,49,8,
%T 13,95,33,53,53,33,95,13,21,177,53,92,45,92,53,177,21,34,359,77,149,
%U 87,87,149,77,359,34,55,705,111,250,150,171,150,250,111,705,55,89,1351,171,426
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0...1...1...2...3...5...8..13..21...34...55...89..144...233...377...610...987
%C ..1...3...7..13..23..49..95.177.359..705.1351.2689.5303.10321.20423.40353.79223
%C ..1...7..15..19..21..33..53..77.111..171..269..415..643..1013..1605..2543..4041
%C ..2..13..19..30..53..92.149.250.426..809.1456.2602.4606..8096.14731.27112.49118
%C ..3..23..21..53..45..87.150.216.249..423..711..980.1560..2431..3368..5598..8655
%C ..5..49..33..92..87.171.203.328.484..782.1106.1905.2833..4428..7210.11516.17938
%C ..8..95..53.149.150.203.229.365.410..734..917.1484.2077..2943..4659..7326.10594
%C .13.177..77.250.216.328.365.417.593..783.1086.1490.1929..2529..3490..4795..6787
%C .21.359.111.426.249.484.410.593.822.1041.1437.2208.3116..4525..6831.10816.16439
%H R. H. Hardin, <a href="/A298093/b298093.txt">Table of n, a(n) for n = 1..1055</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
%F k=3: a(n) = 2*a(n-1) -a(n-4) -a(n-5) -a(n-6) +a(n-7) +a(n-8) for n>9
%F k=4: [order 35] for n>40
%F k=5: [order 82] for n>86
%e Some solutions for n=7 k=4
%e ..0..1..0..0. .0..1..0..0. .0..0..0..1. .0..1..0..1. .0..0..1..0
%e ..0..1..1..1. .1..0..1..1. .0..1..0..1. .0..1..0..1. .1..1..0..1
%e ..1..0..1..0. .0..1..0..1. .1..1..0..0. .0..1..0..1. .1..0..1..0
%e ..1..0..1..0. .1..0..1..1. .1..1..0..0. .1..1..1..0. .1..1..1..0
%e ..0..1..1..1. .0..1..0..0. .0..1..0..1. .0..0..1..0. .1..1..1..0
%e ..0..1..0..0. .1..0..1..0. .1..0..1..0. .1..1..0..1. .1..0..1..0
%e ..0..1..1..0. .1..0..0..0. .0..1..0..1. .1..0..1..0. .0..0..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297852.
%Y Column 3 is A297853.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 12 2018
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