A316545 - OEIS

%I #4 Jul 06 2018 12:27:36

%S 1,2,2,4,4,4,8,12,12,8,16,24,26,24,16,32,64,53,53,64,32,64,184,187,

%T 136,187,184,64,128,432,484,568,568,484,432,128,256,1088,1262,1874,

%U 4219,1874,1262,1088,256,512,2944,3570,5966,19819,19819,5966,3570,2944,512,1024

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2....4.....8......16.......32........64........128..........256

%C ...2....4...12....24......64......184.......432.......1088.........2944

%C ...4...12...26....53.....187......484......1262.......3570.........9751

%C ...8...24...53...136.....568.....1874......5966......20721........70789

%C ..16...64..187...568....4219....19819.....85583.....452386......2248258

%C ..32..184..484..1874...19819...114514....674392....4849500.....31884846

%C ..64..432.1262..5966...85583...674392...5074646...49303976....433518999

%C .128.1088.3570.20721..452386..4849500..49303976..681913008...8395255440

%C .256.2944.9751.70789.2248258.31884846.433518999.8395255440.140688693646

%H R. H. Hardin, <a href="/A316545/b316545.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6

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

%F k=4: [order 34] for n>38

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303794.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 06 2018