A305530 - OEIS

%I #4 Jun 04 2018 12:05:42

%S 1,2,2,4,8,4,8,30,30,8,16,112,161,112,16,32,420,880,880,420,32,64,

%T 1576,4779,7385,4779,1576,64,128,5912,26000,61139,61139,26000,5912,

%U 128,256,22176,141474,506359,767417,506359,141474,22176,256,512,83184,769617

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

%C Table starts

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

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

%C ...4....30.....161.......880........4779.........26000.........141474

%C ...8...112.....880......7385.......61139........506359........4205030

%C ..16...420....4779.....61139......767417.......9599897......120736482

%C ..32..1576...26000....506359.....9599897.....180860170.....3433486971

%C ..64..5912..141474...4205030...120736482....3433486971....98651246976

%C .128.22176..769617..34889423..1516911265...65111777047..2831187189412

%C .256.83184.4187055.289444806.19047231319.1233566348589.81130991759635

%H R. H. Hardin, <a href="/A305530/b305530.txt">Table of n, a(n) for n = 1..180</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]

%F k=4: [order 38] for n>39

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A281949.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 04 2018