A298719 - OEIS

%I #4 Jan 25 2018 08:50:03

%S 0,0,0,0,1,0,0,2,2,0,0,5,4,5,0,0,10,13,13,10,0,0,25,63,59,63,25,0,0,

%T 54,264,346,346,264,54,0,0,125,1005,2246,3508,2246,1005,125,0,0,282,

%U 4113,13650,34704,34704,13650,4113,282,0,0,641,16720,87117,309593,563977

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0.....0......0........0..........0............0.............0

%C .0...1.....2......5.......10.........25...........54...........125

%C .0...2.....4.....13.......63........264.........1005..........4113

%C .0...5....13.....59......346.......2246........13650.........87117

%C .0..10....63....346.....3508......34704.......309593.......2960634

%C .0..25...264...2246....34704.....563977......8287084.....125919136

%C .0..54..1005..13650...309593....8287084....193439202....4672566734

%C .0.125..4113..87117..2960634..125919136...4672566734..177476979652

%C .0.282.16720.550582.27934888.1909040369.112689610775.6748480839625

%H R. H. Hardin, <a href="/A298719/b298719.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

%F k=4: [order 63] for n>64

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297860.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 25 2018