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A297858 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 king-move adjacent elements, with upper left element zero.

%I A297858 #4 Jan 07 2018 10:41:59
%S A297858 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 A297858 13,95,33,53,53,33,95,13,21,177,53,90,45,90,53,177,21,34,359,77,145,
%U A297858 81,81,145,77,359,34,55,705,111,244,130,131,130,244,111,705,55,89,1351,171,406
%N A297858 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 king-move adjacent elements, with upper left element zero.
%C A297858 Table starts
%C A297858 ..0...1...1...2...3...5...8..13..21..34...55...89..144...233...377...610...987
%C A297858 ..1...3...7..13..23..49..95.177.359.705.1351.2689.5303.10321.20423.40353.79223
%C A297858 ..1...7..15..19..21..33..53..77.111.171..269..415..643..1013..1605..2543..4041
%C A297858 ..2..13..19..30..53..90.145.244.406.771.1396.2472.4358..7688.13953.25626.46458
%C A297858 ..3..23..21..53..45..81.130.186.203.313..533..737.1132..1722..2282..3719..5672
%C A297858 ..5..49..33..90..81.131.146.252.320.522..705.1188.1654..2554..4086..6240..9384
%C A297858 ..8..95..53.145.130.146.181.289.294.594..711.1167.1681..2374..3827..6129..8841
%C A297858 .13.177..77.244.186.252.289.298.406.568..780.1009.1299..1639..2169..2986..4144
%C A297858 .21.359.111.406.203.320.294.406.430.614..791.1026.1413..1823..2395..3684..5064
%H A297858 R. H. Hardin, <a href="/A297858/b297858.txt">Table of n, a(n) for n = 1..1104</a>
%F A297858 Empirical for column k:
%F A297858 k=1: a(n) = a(n-1) +a(n-2)
%F A297858 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 A297858 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 A297858 k=4: [order 32] for n>37
%F A297858 k=5: [order 76] for n>81
%e A297858 Some solutions for n=7 k=4
%e A297858 ..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..0..1..0. .0..0..1..0
%e A297858 ..1..1..0..0. .0..1..0..0. .0..0..1..0. .1..0..1..0. .1..1..1..0
%e A297858 ..1..0..1..0. .0..1..1..1. .1..1..1..0. .1..0..0..1. .0..1..0..1
%e A297858 ..1..1..0..0. .1..0..1..0. .0..0..1..1. .0..1..0..1. .0..1..0..1
%e A297858 ..0..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..0..1
%e A297858 ..1..0..0..0. .1..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
%e A297858 ..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1
%Y A297858 Column 1 is A000045(n-1).
%K A297858 nonn,tabl
%O A297858 1,5
%A A297858 _R. H. Hardin_, Jan 07 2018