A317383 - OEIS

%I #4 Jul 26 2018 17:02:09

%S 1,2,2,4,4,4,8,5,5,8,16,9,18,9,16,32,22,36,36,22,32,64,45,94,123,94,

%T 45,64,128,101,270,414,414,270,101,128,256,218,731,1580,2089,1580,731,

%U 218,256,512,477,1973,5704,10732,10732,5704,1973,477,512,1024,1041,5388

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6, 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....5.....9......22.......45.......101........218..........477

%C ...4...5...18....36......94......270.......731.......1973.........5388

%C ...8...9...36...123.....414.....1580......5704......20162........72715

%C ..16..22...94...414....2089....10732.....52617.....260141......1299431

%C ..32..45..270..1580...10732....75405....508181....3446847.....23624322

%C ..64.101..731..5704...52617...508181...4726521...44156330....416173164

%C .128.218.1973.20162..260141..3446847..44156330..569899203...7400913778

%C .256.477.5388.72715.1299431.23624322.416173164.7400913778.132364711390

%H R. H. Hardin, <a href="/A317383/b317383.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +3*a(n-2) +5*a(n-3) +2*a(n-4) -3*a(n-5) -10*a(n-6) -8*a(n-7) for n>10

%F k=4: [order 19] for n>23

%F k=5: [order 43] for n>49

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A052962 for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 26 2018