A223576 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal.

3, 9, 9, 27, 81, 27, 81, 729, 729, 81, 243, 6561, 16038, 6561, 243, 729, 59049, 352836, 352836, 59049, 729, 2187, 531441, 7762392, 16230456, 7762392, 531441, 2187, 6561, 4782969, 170772624, 746600976, 746600976, 170772624, 4782969, 6561, 19683

Offset: 1

Author

R. H. Hardin Mar 22 2013

Keywords

• nonn
• tabl

Comments

Table starts

.....3..........9.............27.................81...................243

.....9.........81............729...............6561.................59049

....27........729..........16038.............352836...............7762392

....81.......6561.........352836...........16230456.............746600976

...243......59049........7762392..........746600976...........64207683936

...729.....531441......170772624........34343644896.........5521860818496

..2187....4782969.....3756997728......1579807665216.......474880030390656

..6561...43046721....82653950016.....72671152599936.....40839682613596416

.19683..387420489..1818386900352...3342873019597056...3512212704769291776

.59049.3486784401.40004511807744.153772158901464576.302050292610159092736

Examples

			Some solutions for n=3 k=4
..0..1..2..2....0..2..0..1....0..1..2..2....0..0..1..2....0..1..0..2
..0..1..2..2....1..1..2..0....1..1..0..1....1..2..1..2....0..2..1..0
..1..2..1..1....1..2..0..1....1..0..2..2....1..0..2..0....0..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1000

Crossrefs

Column 1 is A000244

Column 2 is A001019

Formula

Let U(z) = (z^4+6*z^3+23*z^2+18*z+24)/24

T(n,k) = U(min(n,k))^(max(n,k)-min(n,k)+1) * product{ U(i)^2 , i=1..(min(n,k)-1) }