%I #4 May 21 2018 09:16:42

%S 1,2,2,4,4,4,8,5,5,8,16,9,15,9,16,32,22,31,31,22,32,64,45,73,87,73,45,

%T 64,128,101,191,266,266,191,101,128,256,218,466,851,1054,851,466,218,

%U 256,512,477,1125,2510,4186,4186,2510,1125,477,512,1024,1041,2762,7348,16158

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1...2....4.....8.....16......32.......64.......128........256.........512

%C ...2...4....5.....9.....22......45......101.......218........477........1041

%C ...4...5...15....31.....73.....191......466......1125.......2762........6805

%C ...8...9...31....87....266.....851.....2510......7348......21910.......65581

%C ..16..22...73...266...1054....4186....16158.....63555.....251536......988178

%C ..32..45..191...851...4186...21214...104451....524286....2629697....13159898

%C ..64.101..466..2510..16158..104451...649029...4123792...26044218...164807242

%C .128.218.1125..7348..63555..524286..4123792..33757130..273455401..2220694647

%C .256.477.2762.21910.251536.2629697.26044218.273455401.2831764125.29378878160

%H R. H. Hardin, <a href="/A304926/b304926.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) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6

%F k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>9

%F k=4: [order 13] for n>18

%F k=5: [order 34] for n>41

%F k=6: [order 96] for n>103

%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..1..1..1

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

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

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

%e ..0..0..1..0. .0..0..0..1. .0..0..1..0. .0..1..0..0. .1..0..1..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_, May 21 2018