%I #5 Mar 31 2012 12:36:46

%S 4,4,4,4,30,4,4,72,72,4,4,131,1372,131,4,4,208,9260,9260,208,4,4,304,

%T 38112,408599,38112,304,4,4,420,117744,8002304,8002304,117744,420,4,4,

%U 557,301612,91893727,858105364,91893727,301612,557,4,4,716,676792

%N T(n,k)=Number of nXk 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards

%C Table starts

%C .4...4.......4...........4...............4..................4

%C .4..30......72.........131.............208................304

%C .4..72....1372........9260...........38112.............117744

%C .4.131....9260......408599.........8002304...........91893727

%C .4.208...38112.....8002304.......858105364........48452117136

%C .4.304..117744....91893727.....48452117136.....13486744809160

%C .4.420..301612...729771318...1706069013928...2238761872232964

%C .4.557..676792..4412536785..41801237632858.248685266018356303

%C .4.716.1375740.21616887220.764295988745248

%C .4.898.2589832.89573637672

%H R. H. Hardin, <a href="/A201981/b201981.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical: rows (and columns) 2,3,4,5 are polynomials of degree 3,6,18,30

%e Some solutions for n=5 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 07 2011