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A280859 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%I A280859 #4 Jan 09 2017 09:38:21
%S A280859 1,2,2,4,9,4,11,29,29,11,30,110,46,110,30,82,442,96,96,442,82,224,
%T A280859 1708,256,124,256,1708,224,612,6596,678,216,216,678,6596,612,1672,
%U A280859 25624,1698,462,282,462,1698,25624,1672,4568,99432,4358,1005,491,491,1005,4358
%N A280859 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
%C A280859 Table starts
%C A280859 ....1......2.....4...11...30...82..224...612..1672...4568...12480...34096
%C A280859 ....2......9....29..110..442.1708.6596.25624.99432.385584.1495696.5802080
%C A280859 ....4.....29....46...96..256..678.1698..4358.11218..28650...73354..188066
%C A280859 ...11....110....96..124..216..462.1005..2010..3907...7756...15749...31804
%C A280859 ...30....442...256..216..282..491..968..1857..3220...5281....8574...14339
%C A280859 ...82...1708...678..462..491..712.1202..2268..4220...7108...11240...17330
%C A280859 ..224...6596..1698.1005..968.1202.1738..2877..5244...9569...15872...24653
%C A280859 ..612..25624..4358.2010.1857.2268.2877..4124..6722..12044...21713...35572
%C A280859 .1672..99432.11218.3907.3220.4220.5244..6722..9562..15351...27000...48087
%C A280859 .4568.385584.28650.7756.5281.7108.9569.12044.15351..21752...34547...59836
%H A280859 R. H. Hardin, <a href="/A280859/b280859.txt">Table of n, a(n) for n = 1..480</a>
%F A280859 Empirical for column k:
%F A280859 k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F A280859 k=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
%F A280859 k=3: a(n) = 2*a(n-1) +4*a(n-3) -a(n-4) +2*a(n-6) -2*a(n-7) for n>9
%F A280859 k=4: [order 12] for n>16
%F A280859 k=5: [order 12] for n>18
%F A280859 k=6: [order 16] for n>22
%F A280859 k=7: [order 23] for n>29
%e A280859 Some solutions for n=4 k=4
%e A280859 ..0..1..1..2. .0..1..0..0. .0..1..2..2. .0..0..1..1. .0..0..1..0
%e A280859 ..2..2..0..2. .0..2..2..1. .0..1..0..1. .1..2..2..0. .1..2..1..2
%e A280859 ..0..1..0..1. .1..1..0..1. .2..2..0..2. .1..0..1..0. .0..2..0..2
%e A280859 ..2..1..2..2. .2..0..2..2. .0..1..1..2. .2..2..1..2. .0..1..0..1
%Y A280859 Column 1 is A021006(n-3).
%K A280859 nonn,tabl
%O A280859 1,2
%A A280859 _R. H. Hardin_, Jan 09 2017