A306136 - OEIS

%I #4 Jun 22 2018 07:45:05

%S 1,1,1,1,4,1,1,8,8,1,1,24,13,24,1,1,82,64,64,82,1,1,272,240,498,240,

%T 272,1,1,908,842,2922,2922,842,908,1,1,3076,3302,16877,31843,16877,

%U 3302,3076,1,1,10444,12740,111073,267988,267988,111073,12740,10444,1,1,35480,48468

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

%C Table starts

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

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

%C .1.....8....13......64.......240.........842.........3302..........12740

%C .1....24....64.....498......2922.......16877.......111073.........700859

%C .1....82...240....2922.....31843......267988......2889140.......29281552

%C .1...272...842...16877....267988.....3176303.....50158767......730698959

%C .1...908..3302..111073...2889140....50158767...1284005626....29447872807

%C .1..3076.12740..700859..29281552...730698959..29447872807..1028875496355

%C .1.10444.48468.4405884.289967701.10451513277.652802237683.34579655304548

%H R. H. Hardin, <a href="/A306136/b306136.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) = 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 20]

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

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A303882.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jun 22 2018