%I #4 Jan 24 2018 10:01:00

%S 0,1,1,1,4,1,2,17,17,2,3,49,48,49,3,5,166,146,146,166,5,8,573,424,466,

%T 424,573,8,13,1933,1274,1446,1446,1274,1933,13,21,6538,3820,4648,5124,

%U 4648,3820,6538,21,34,22165,11529,14888,18271,18271,14888,11529,22165,34

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.....1......2......3.......5........8........13.........21.........34

%C ..1.....4....17.....49....166.....573.....1933......6538......22165......75089

%C ..1....17....48....146....424....1274.....3820.....11529......34783.....104826

%C ..2....49...146....466...1446....4648....14888.....47399.....150849.....480015

%C ..3...166...424...1446...5124...18271....62544....215035.....739962....2537660

%C ..5...573..1274...4648..18271...75562...291784...1142188....4518674...17656883

%C ..8..1933..3820..14888..62544..291784..1277500...5758443...26328879..118276552

%C .13..6538.11529..47399.215035.1142188..5758443..30337435..163931288..865848465

%C .21.22165.34783.150849.739962.4518674.26328879.163931288.1060912744.6689007779

%H R. H. Hardin, <a href="/A298653/b298653.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

%F k=3: [order 11] for n>13

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

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A297817.

%Y Column 3 is A297988.

%Y Column 4 is A297989.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 24 2018