A316183 - OEIS

%I #4 Jun 25 2018 17:49:32

%S 1,2,2,4,8,4,8,30,30,8,16,112,134,112,16,32,420,601,601,420,32,64,

%T 1576,2665,3653,2665,1576,64,128,5912,11915,21825,21825,11915,5912,

%U 128,256,22176,53134,134426,168051,134426,53134,22176,256,512,83184,237241

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2.......4........8........16..........32...........64............128

%C ...2.....8......30......112.......420........1576.........5912..........22176

%C ...4....30.....134......601......2665.......11915........53134.........237241

%C ...8...112.....601.....3653.....21825......134426.......822258........5056910

%C ..16...420....2665....21825....168051.....1361115.....11056918.......90607484

%C ..32..1576...11915...134426...1361115....14569771....157538845.....1721566496

%C ..64..5912...53134...822258..11056918...157538845...2280994876....33428704605

%C .128.22176..237241..5056910..90607484..1721566496..33428704605...658322110177

%C .256.83184.1058821.31069974.744476711.18934361346.494144449793.13102040590991

%H R. H. Hardin, <a href="/A316183/b316183.txt">Table of n, a(n) for n = 1..240</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

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

%F k=3: [order 11] for n>12

%F k=4: [order 30] for n>34

%F k=5: [order 74] for n>79

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A281949.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 25 2018