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A298970 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

%I A298970 #4 Jan 30 2018 13:31:58
%S A298970 1,2,2,4,8,4,8,32,32,8,16,128,219,128,16,32,512,1575,1575,512,32,64,
%T A298970 2048,11283,21098,11283,2048,64,128,8192,80972,280468,280468,80972,
%U A298970 8192,128,256,32768,581057,3740381,6892031,3740381,581057,32768,256,512,131072
%N A298970 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
%C A298970 Table starts
%C A298970 ...1.....2.......4.........8...........16.............32...............64
%C A298970 ...2.....8......32.......128..........512...........2048.............8192
%C A298970 ...4....32.....219......1575........11283..........80972...........581057
%C A298970 ...8...128....1575.....21098.......280468........3740381.........49885231
%C A298970 ..16...512...11283....280468......6892031......170137416.......4200575252
%C A298970 ..32..2048...80972...3740381....170137416.....7785598672.....356356552103
%C A298970 ..64..8192..581057..49885231...4200575252...356356552103...30241030285680
%C A298970 .128.32768.4169867.665351771.103715870545.16312003284843.2566506415636896
%H A298970 R. H. Hardin, <a href="/A298970/b298970.txt">Table of n, a(n) for n = 1..180</a>
%F A298970 Empirical for column k:
%F A298970 k=1: a(n) = 2*a(n-1)
%F A298970 k=2: a(n) = 4*a(n-1)
%F A298970 k=3: [order 8]
%F A298970 k=4: [order 23]
%F A298970 k=5: [order 75]
%e A298970 Some solutions for n=5 k=4
%e A298970 ..0..0..0..1. .0..0..1..1. .0..0..0..1. .0..0..1..0. .0..0..0..0
%e A298970 ..1..1..0..1. .0..0..0..0. .1..0..0..0. .1..1..1..0. .0..0..1..0
%e A298970 ..0..1..0..1. .0..1..1..1. .1..1..0..1. .1..1..0..1. .0..1..1..0
%e A298970 ..0..0..0..1. .1..1..0..1. .1..1..1..0. .1..0..0..0. .1..1..0..1
%e A298970 ..0..1..1..0. .0..0..1..0. .0..0..0..1. .1..1..1..0. .1..0..0..1
%Y A298970 Column 1 is A000079(n-1).
%Y A298970 Column 2 is A004171(n-1).
%K A298970 nonn,tabl
%O A298970 1,2
%A A298970 _R. H. Hardin_, Jan 30 2018