A282791 - OEIS

%I #4 Feb 21 2017 08:46:40

%S 0,0,0,1,0,1,2,8,8,2,5,16,73,16,5,12,72,318,318,72,12,26,240,1747,

%T 1952,1747,240,26,56,736,8216,16584,16584,8216,736,56,118,2352,38027,

%U 119176,208559,119176,38027,2352,118,244,7128,173722,832218,2207352,2207352

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

%C Table starts

%C ...0.....0.......1.........2...........5............12..............26

%C ...0.....0.......8........16..........72...........240.............736

%C ...1.....8......73.......318........1747..........8216...........38027

%C ...2....16.....318......1952.......16584........119176..........832218

%C ...5....72....1747.....16584......208559.......2207352........22998587

%C ..12...240....8216....119176.....2207352......34974844.......545174028

%C ..26...736...38027....832218....22998587.....545174028.....12713143876

%C ..56..2352..173722...5780340...236744562....8385651160....292288389872

%C .118..7128..773529..39020884..2372235577..125782952202...6555156469894

%C .244.21424.3412416.260919192.23556868268.1869100531456.145619095090322

%H R. H. Hardin, <a href="/A282791/b282791.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)

%F k=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)

%F k=3: [order 12]

%F k=4: [order 18]

%F k=5: [order 42]

%F k=6: [order 60]

%e Some solutions for n=4 k=4

%e ..0..1..0..0. .0..1..0..1. .0..1..0..0. .0..0..1..1. .1..0..1..0

%e ..1..0..0..1. .0..0..1..0. .1..0..0..1. .0..1..0..0. .0..0..1..0

%e ..0..1..0..0. .1..0..0..0. .0..0..1..0. .0..0..0..1. .0..0..0..0

%e ..0..0..0..0. .1..0..1..0. .1..0..0..1. .0..1..0..0. .1..1..1..0

%Y Column 1 is A073778(n-1).

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_, Feb 21 2017