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A280362 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.

%I A280362 #4 Jan 01 2017 08:57:52
%S A280362 1,2,2,4,9,4,11,50,50,11,30,285,571,285,30,82,1617,6727,6727,1617,82,
%T A280362 224,9188,78800,164326,78800,9188,224,612,52193,924579,3992071,
%U A280362 3992071,924579,52193,612,1672,296511,10844773,97147710,201054068,97147710
%N A280362 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.
%C A280362 Table starts
%C A280362 ....1.......2...........4.............11...............30................82
%C A280362 ....2.......9..........50............285.............1617..............9188
%C A280362 ....4......50.........571...........6727............78800............924579
%C A280362 ...11.....285........6727.........164326..........3992071..........97147710
%C A280362 ...30....1617.......78800........3992071........201054068.......10144351660
%C A280362 ...82....9188......924579.......97147710......10144351660.....1061399606602
%C A280362 ..224...52193....10844773.....2363431872.....511688896140...111020011111453
%C A280362 ..612..296511...127214104....57503068637...25812250379197.11613529410292966
%C A280362 .1672.1684466..1492251709..1399048151083.1302084964081326
%C A280362 .4568.9569425.17504551617.34038954765446
%H A280362 R. H. Hardin, <a href="/A280362/b280362.txt">Table of n, a(n) for n = 1..97</a>
%F A280362 Empirical for column k:
%F A280362 k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F A280362 k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
%F A280362 k=3: [order 12]
%F A280362 k=4: [order 44]
%e A280362 Some solutions for n=4 k=4
%e A280362 ..0..1..2..1. .0..0..1..2. .0..1..2..0. .0..1..2..0. .0..1..0..2
%e A280362 ..0..2..1..0. .1..2..0..2. .0..2..1..2. .1..0..2..1. .0..2..1..2
%e A280362 ..1..0..0..1. .2..1..2..1. .1..1..2..1. .0..2..0..1. .2..1..2..1
%e A280362 ..0..2..2..1. .0..1..2..0. .0..0..1..0. .0..1..1..0. .2..0..2..1
%Y A280362 Column 1 is A021006(n-3).
%Y A280362 Column 2 is A231413(n-1).
%K A280362 nonn,tabl
%O A280362 1,2
%A A280362 _R. H. Hardin_, Jan 01 2017