%I
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,69,27,27,69,32,64,137,43,41,
%T 43,137,64,128,301,70,101,101,70,301,128,256,705,106,158,178,158,106,
%U 705,256,512,1461,169,263,253,253,263,169,1461,512,1024,3193,276,481,423,388
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 7 kingmove adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2...4...8...16...32...64..128..256..512.1024..2048..4096..8192..16384
%C ...2....7..13..29...69..137..301..705.1461.3193.7373.15729.34405.78569.170813
%C ...4...13..20..27...43...70..106..169..276..444..720..1183..1947..3207...5311
%C ...8...29..27..41..101..158..263..481..776.1387.2567..4539..8077.14329..25589
%C ..16...69..43.101..178..253..423..715.1082.1821.3203..5330..8978.15692..26461
%C ..32..137..70.158..253..388..434..830.1351.1892.3026..5492..8206.13206..23026
%C ..64..301.106.263..423..434..628.1067.1267.1943.2973..4583..6623.10201..15735
%C .128..705.169.481..715..830.1067.1708.2118.2978.4984..7136.10725.17602..27551
%C .256.1461.276.776.1082.1351.1267.2118.2860.3333.5106..7796.10253.15979..24788
%H R. H. Hardin, <a href="/A298494/b298494.txt">Table of n, a(n) for n = 1..1010</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n1)
%F k=2: a(n) = 3*a(n1) 2*a(n2) +8*a(n3) 20*a(n4) +8*a(n5) for n>6
%F k=3: [order 11] for n>12
%F k=4: [order 41] for n>43
%e Some solutions for n=9 k=4
%e ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..0..1..0
%e ..1..1..0..0. .1..0..1..1. .1..0..1..0. .1..1..1..1. .1..1..0..1
%e ..1..1..0..0. .0..1..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1
%e ..0..1..0..1. .0..1..1..1. .1..0..1..0. .1..1..1..1. .1..0..1..0
%e ..1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..1..0. .1..0..1..0
%e ..0..1..0..1. .0..0..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
%e ..1..1..0..0. .1..0..0..0. .1..1..0..0. .0..0..0..0. .0..1..1..1
%e ..1..1..0..0. .1..0..1..1. .0..1..0..1. .1..0..0..1. .0..1..0..0
%e ..0..1..0..1. .1..0..0..1. .1..0..1..0. .0..0..0..0. .0..1..1..0
%Y Column 1 is A000079(n1).
%Y Column 2 is A297883.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 20 2018
