A305281 - OEIS

%I #4 May 29 2018 08:05:58

%S 1,1,1,1,4,1,1,8,8,1,1,24,11,24,1,1,82,36,36,82,1,1,272,87,166,87,272,

%T 1,1,908,256,487,487,256,908,1,1,3076,684,2130,1185,2130,684,3076,1,1,

%U 10444,1932,7433,5060,5060,7433,1932,10444,1,1,35480,5308,30191,17335

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .1.....1....1......1......1.......1.......1........1.........1..........1

%C .1.....4....8.....24.....82.....272.....908.....3076.....10444......35480

%C .1.....8...11.....36.....87.....256.....684.....1932......5308......14809

%C .1....24...36....166....487....2130....7433....30191....112815.....444834

%C .1....82...87....487...1185....5060...17335....73058....275241....1135214

%C .1...272..256...2130...5060...26577...96739...437098...1790654....7846313

%C .1...908..684...7433..17335...96739..342596..1733499...7108688...34070865

%C .1..3076.1932..30191..73058..437098.1733499..9804507..44808093..246735199

%C .1.10444.5308.112815.275241.1790654.7108688.44808093.220905716.1340680187

%H R. H. Hardin, <a href="/A305281/b305281.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

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

%F k=3: [order 16] for n>18

%F k=4: [order 38] for n>41

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A303882.

%Y Column 3 is A303883.

%Y Column 4 is A303884.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 29 2018