A224024 - OEIS

%I #4 Mar 30 2013 10:17:23

%S 4,10,16,20,100,64,35,400,1000,256,56,1225,6796,10000,1024,84,3136,

%T 32523,112436,100000,4096,120,7056,122523,772683,1859020,1000000,

%U 16384,165,14400,387729,4002738,17735200,30756756,10000000,65536,220,27225,1074167

%N T(n,k)=Number of nXk 0..3 arrays with rows nondecreasing and antidiagonals unimodal

%C Table starts

%C .......4..........10............20..............35...............56

%C ......16.........100...........400............1225.............3136

%C ......64........1000..........6796...........32523...........122523

%C .....256.......10000........112436..........772683..........4002738

%C ....1024......100000.......1859020........17735200........120352359

%C ....4096.....1000000......30756756.......403836633.......3491241557

%C ...16384....10000000.....508916456......9186127249......99853876444

%C ...65536...100000000....8420768936....208983591829....2841637297963

%C ..262144..1000000000..139333478144...4754911670136...80738139650660

%C .1048576.10000000000.2305467501680.108190494364824.2292943314015674

%H R. H. Hardin, <a href="/A224024/b224024.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical: columns k=1..7 have recurrences of order 1,1,7,10,19,25,41

%F Empirical: rows n=1..7 are polynomials of degree 3*n for k>0,0,1,2,3,4,5

%e Some solutions for n=3 k=4

%e ..3..3..3..3....1..3..3..3....0..0..0..2....1..1..2..2....0..0..1..1

%e ..0..2..3..3....0..2..3..3....2..2..3..3....0..0..1..2....0..1..3..3

%e ..1..1..1..1....0..0..1..1....0..2..2..3....0..0..2..3....1..1..3..3

%Y Column 1 is A000302

%Y Column 2 is A011557

%Y Row 1 is A000292(n+1)

%Y Row 2 is A001249

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 30 2013