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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. 5

%I #4 Jan 01 2017 08:57:52

%S 1,2,2,4,9,4,11,50,50,11,30,285,571,285,30,82,1617,6727,6727,1617,82,

%T 224,9188,78800,164326,78800,9188,224,612,52193,924579,3992071,

%U 3992071,924579,52193,612,1672,296511,10844773,97147710,201054068,97147710

%N 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 Table starts

%C ....1.......2...........4.............11...............30................82

%C ....2.......9..........50............285.............1617..............9188

%C ....4......50.........571...........6727............78800............924579

%C ...11.....285........6727.........164326..........3992071..........97147710

%C ...30....1617.......78800........3992071........201054068.......10144351660

%C ...82....9188......924579.......97147710......10144351660.....1061399606602

%C ..224...52193....10844773.....2363431872.....511688896140...111020011111453

%C ..612..296511...127214104....57503068637...25812250379197.11613529410292966

%C .1672.1684466..1492251709..1399048151083.1302084964081326

%C .4568.9569425.17504551617.34038954765446

%H R. H. Hardin, <a href="/A280362/b280362.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4

%F k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5

%F k=3: [order 12]

%F k=4: [order 44]

%e Some solutions for n=4 k=4

%e ..0..1..2..1. .0..0..1..2. .0..1..2..0. .0..1..2..0. .0..1..0..2

%e ..0..2..1..0. .1..2..0..2. .0..2..1..2. .1..0..2..1. .0..2..1..2

%e ..1..0..0..1. .2..1..2..1. .1..1..2..1. .0..2..0..1. .2..1..2..1

%e ..0..2..2..1. .0..1..2..0. .0..0..1..0. .0..1..1..0. .2..0..2..1

%Y Column 1 is A021006(n-3).

%Y Column 2 is A231413(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jan 01 2017

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Last modified March 5 08:40 EST 2024. Contains 370538 sequences. (Running on oeis4.)