A299458 - OEIS

%I #4 Feb 10 2018 10:37:57

%S 1,1,1,1,5,1,1,7,7,1,1,18,7,18,1,1,31,19,19,31,1,1,65,35,48,35,65,1,1,

%T 130,95,175,175,95,130,1,1,253,223,508,1015,508,223,253,1,1,519,571,

%U 1522,3514,3514,1522,571,519,1,1,1018,1535,5065,14409,19041,14409,5065,1535

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5, 6 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...5....7....18.....31......65......130.......253.........519.........1018

%C .1...7....7....19.....35......95......223.......571........1535.........4091

%C .1..18...19....48....175.....508.....1522......5065.......16968........56041

%C .1..31...35...175...1015....3514....14409.....69402......304094......1294490

%C .1..65...95...508...3514...19041...101878....624052.....3827796.....22241786

%C .1.130..223..1522..14409..101878...750083...6104533....48998539....384601868

%C .1.253..571..5065..69402..624052..6104533..67847199...723450111...7524339497

%C .1.519.1535.16968.304094.3827796.48998539.723450111.10455199270.145448283457

%H R. H. Hardin, <a href="/A299458/b299458.txt">Table of n, a(n) for n = 1..197</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 18] for n>19

%F k=4: [order 70] for n>71

%e Some solutions for n=6 k=6

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

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

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

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

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

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

%Y Column 2 is A297937.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 10 2018