A298287 - OEIS

%I #4 Jan 16 2018 08:26:00

%S 1,2,2,4,8,4,8,25,25,8,16,85,70,85,16,32,286,205,205,286,32,64,969,

%T 614,649,614,969,64,128,3281,1860,2151,2151,1860,3281,128,256,11114,

%U 5631,7006,8264,7006,5631,11114,256,512,37649,17034,22768,29673,29673,22768

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

%C Table starts

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

%C ...2.....8....25.....85.....286.....969.....3281.....11114......37649

%C ...4....25....70....205.....614....1860.....5631.....17034......51507

%C ...8....85...205....649....2151....7006....22768.....73751.....238775

%C ..16...286...614...2151....8264...29673...104357....369220....1307146

%C ..32...969..1860...7006...29673..121368...484412...1948367....7872325

%C ..64..3281..5631..22768..104357..484412..2195114..10198130...48049615

%C .128.11114.17034..73751..369220.1948367.10198130..55665676..310280107

%C .256.37649.51507.238775.1307146.7872325.48049615.310280107.2065512284

%H R. H. Hardin, <a href="/A298287/b298287.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

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

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

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

%F k=4: [order 24] for n>27

%e Some solutions for n=6 k=4

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

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

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

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

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

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

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

%Y Column 2 is A281338.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 16 2018