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A299740 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

%I A299740 #4 Feb 18 2018 10:16:09
%S A299740 1,2,2,4,8,4,8,32,32,8,16,128,220,128,16,32,512,1578,1578,512,32,64,
%T A299740 2048,11303,21111,11303,2048,64,128,8192,81105,280642,280642,81105,
%U A299740 8192,128,256,32768,582032,3742524,6896530,3742524,582032,32768,256,512,131072
%N A299740 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C A299740 Table starts
%C A299740 ...1.....2.......4.........8...........16.............32...............64
%C A299740 ...2.....8......32.......128..........512...........2048.............8192
%C A299740 ...4....32.....220......1578........11303..........81105...........582032
%C A299740 ...8...128....1578.....21111.......280642........3742524.........49914496
%C A299740 ..16...512...11303....280642......6896530......170243005.......4203272237
%C A299740 ..32..2048...81105...3742524....170243005.....7790212998.....356575568843
%C A299740 ..64..8192..582032..49914496...4203272237...356575568843...30260326859957
%C A299740 .128.32768.4177161.665759775.103785926879.16322570202905.2568233775595684
%H A299740 R. H. Hardin, <a href="/A299740/b299740.txt">Table of n, a(n) for n = 1..180</a>
%F A299740 Empirical for column k:
%F A299740 k=1: a(n) = 2*a(n-1)
%F A299740 k=2: a(n) = 4*a(n-1)
%F A299740 k=3: [order 8]
%F A299740 k=4: [order 24]
%F A299740 k=5: [order 79]
%e A299740 Some solutions for n=5 k=4
%e A299740 ..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
%e A299740 ..0..0..0..1. .0..0..0..1. .1..1..1..0. .0..0..0..1. .0..0..0..0
%e A299740 ..0..0..0..1. .1..1..1..0. .0..0..0..1. .1..1..0..0. .0..0..0..0
%e A299740 ..1..1..1..0. .0..0..0..0. .0..0..0..1. .1..0..1..0. .1..1..1..1
%e A299740 ..1..1..1..0. .1..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..1..1
%Y A299740 Column 1 is A000079(n-1).
%Y A299740 Column 2 is A004171(n-1).
%K A299740 nonn,tabl
%O A299740 1,2
%A A299740 _R. H. Hardin_, Feb 18 2018