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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors
16

%I #9 Sep 10 2024 12:38:01

%S 6,26,12,98,82,36,378,514,676,96,1512,3358,9604,4338,264,6018,22396,

%T 142884,130890,29380,720,23890,148820,2286144,4140964,1876940,196698,

%U 1968,94846,990458,36216324,141857204,127574544,26726740,1321986,5376

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors

%H R. H. Hardin, <a href="/A239178/b239178.txt">Table of n, a(n) for n = 1..112</a>

%H N. H. Bong, C. Dalfó, and M. À. Fiol, and D. Závacká, <a href="https://arxiv.org/abs/2409.02125">Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences</a>, arXiv:2409.02125 [math.CO], 2024. See p. 19.

%F Empirical for column k:

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

%F k=2: [order 19]

%F k=3: [order 67]

%F Empirical for row n:

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

%F n=2: [order 31]

%F n=3: [order 21]

%e Some solutions for n=3 k=4

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

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

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

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

%e Table starts

%e ....6......26.........98...........378.............1512................6018

%e ...12......82........514..........3358............22396..............148820

%e ...36.....676.......9604........142884..........2286144............36216324

%e ...96....4338.....130890.......4140964........141857204..........4845741276

%e ..264...29380....1876940.....127574544.......9704723126........733415243746

%e ..720..196698...26726740....3901908720.....652274371446.....108383467365104

%e .1968.1321986..381984614..119751372066...44086966064930...16126266923705212

%e .5376.8867938.5442841504.3664449484670.2970697967221324.2391741572658733884

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 11 2014