%I #6 Apr 26 2021 14:41:05
%S 1,2,2,4,4,4,8,14,14,8,16,28,35,28,16,32,94,98,98,94,32,64,284,358,
%T 396,358,284,64,128,752,1124,2075,2075,1124,752,128,256,2244,3534,
%U 9140,15460,9140,3534,2244,256,512,6532,11667,40412,86944,86944,40412,11667,6532
%N T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2, 4, 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
%C ...2....4....14.....28.......94.......284........752........2244..........6532
%C ...4...14....35.....98......358......1124.......3534.......11667.........37816
%C ...8...28....98....396.....2075......9140......40412......189729........873060
%C ..16...94...358...2075....15460.....86944.....505624.....3261562......20076871
%C ..32..284..1124...9140....86944....595490....4408093....36427606.....282035936
%C ..64..752..3534..40412...505624...4408093...42789430...473649265....4825821471
%C .128.2244.11667.189729..3261562..36427606..473649265..7157370110...96982248284
%C .256.6532.37816.873060.20076871.282035936.4825821471.96982248284.1710658272713
%H R. H. Hardin, <a href="/A305911/b305911.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1);
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n > 6;
%F k=3: [order 15] for n > 16;
%F k=4: [order 69] for n > 70.
%e Some solutions for n=5, k=4
%e ..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..0..0. .0..0..0..1
%e ..0..1..1..0. .0..0..0..0. .0..1..1..0. .0..0..0..1. .1..0..0..1
%e ..1..1..1..1. .0..0..0..0. .1..1..1..0. .0..0..0..1. .0..0..0..0
%e ..0..1..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..0..0..0
%e ..1..1..0..0. .1..1..1..1. .1..0..1..0. .0..0..1..1. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A304341.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 14 2018