A305223 - OEIS

%I #4 May 27 2018 17:37:50

%S 0,0,0,0,3,0,0,4,4,0,0,9,8,9,0,0,18,15,15,18,0,0,33,31,49,31,33,0,0,

%T 72,92,170,170,92,72,0,0,133,264,581,792,581,264,133,0,0,278,784,2184,

%U 3759,3759,2184,784,278,0,0,541,2378,7680,18876,32193,18876,7680,2378,541,0,0

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

%C Table starts

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

%C .0...3....4.....9.....18.......33........72........133.........278

%C .0...4....8....15.....31.......92.......264........784........2378

%C .0...9...15....49....170......581......2184.......7680.......28315

%C .0..18...31...170....792.....3759.....18876......90956......474685

%C .0..33...92...581...3759....32193....212231....1501520....11428272

%C .0..72..264..2184..18876...212231...1893682...18341237...187726549

%C .0.133..784..7680..90956..1501520..18341237..246793217..3592452354

%C .0.278.2378.28315.474685.11428272.187726549.3592452354.75341044066

%H R. H. Hardin, <a href="/A305223/b305223.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 15] for n>18

%F k=4: [order 65] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A304257.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 27 2018