A300096 - OEIS

%I #6 Feb 25 2018 06:22:18

%S 1,1,1,1,5,1,1,7,7,1,1,18,7,18,1,1,31,19,19,31,1,1,65,35,56,35,65,1,1,

%T 130,95,203,203,95,130,1,1,253,225,672,1301,672,225,253,1,1,519,575,

%U 2168,5953,5953,2168,575,519,1,1,1018,1563,7287,27614,43848,27614,7287,1563

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C .1...5....7....18.....31.......65.......130.........253..........519

%C .1...7....7....19.....35.......95.......225.........575.........1563

%C .1..18...19....56....203......672......2168........7287........25652

%C .1..31...35...203...1301.....5953.....27614......144519.......776608

%C .1..65...95...672...5953....43848....310762.....2373454.....19198301

%C .1.130..225..2168..27614...310762...3273425....36840985....436133886

%C .1.253..575..7287.144519..2373454..36840985...616964357..10746198229

%C .1.519.1563.25652.776608.19198301.436133886.10746198229.279529477217

%H R. H. Hardin, <a href="/A300096/b300096.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) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

%F k=3: [order 19] for n>20

%F k=4: [order 71] for n>72

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297937.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 24 2018