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A298924 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%I A298924 #4 Jan 29 2018 08:00:07
%S A298924 0,1,1,0,4,0,1,4,4,1,0,8,1,8,0,1,32,2,2,32,1,0,32,3,3,3,32,0,1,64,5,7,
%T A298924 7,5,64,1,0,256,8,6,9,6,8,256,0,1,256,16,9,12,12,9,16,256,1,0,512,21,
%U A298924 20,17,19,17,20,21,512,0,1,2048,34,22,41,22,22,41,22,34,2048,1,0,2048,55,35,42
%N A298924 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C A298924 Table starts
%C A298924 .0...1..0..1..0..1..0...1...0...1....0....1....0.....1.....0.....1......0
%C A298924 .1...4..4..8.32.32.64.256.256.512.2048.2048.4096.16384.16384.32768.131072
%C A298924 .0...4..1..2..3..5..8..16..21..34...55...89..144...236...377...610....987
%C A298924 .1...8..2..3..7..6..9..20..22..35...59...90..145...240...378...611....991
%C A298924 .0..32..3..7..9.12.17..41..42..67..109..172..277...461...722..1167...1889
%C A298924 .1..32..5..6.12.19.22..48..53.103..169..272..446...863..1346..2395...4154
%C A298924 .0..64..8..9.17.22.31..83..92.172..309..549..923..1830..3021..5580..10091
%C A298924 .1.256.16.20.41.48.83.199.225.460..943.1570.2795..5933.10113.19462..37621
%C A298924 .0.256.21.22.42.53.92.225.330.644.1348.2306.4339..9315.17574.35170..70446
%H A298924 R. H. Hardin, <a href="/A298924/b298924.txt">Table of n, a(n) for n = 1..543</a>
%F A298924 Empirical for column k:
%F A298924 k=1: a(n) = a(n-2)
%F A298924 k=2: a(n) = 8*a(n-3)
%F A298924 k=3: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
%F A298924 k=4: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
%F A298924 k=5: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8) for n>11
%e A298924 Some solutions for n=5 k=4
%e A298924 ..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
%e A298924 ..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
%e A298924 ..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
%e A298924 ..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
%e A298924 ..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
%Y A298924 Column 2 is A096252(n-1).
%K A298924 nonn,tabl
%O A298924 1,5
%A A298924 _R. H. Hardin_, Jan 29 2018