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

1,1

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

Links

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

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) }

Example

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

Crossrefs

Column 1 is A000244

Column 2 is A001019

Sequence in context: A268026 A268019 A228977 * A125824 A203558 A223653

Adjacent sequences: A223573 A223574 A223575 * A223577 A223578 A223579

Keyword

nonn,tabl

Author

R. H. Hardin Mar 22 2013

Status

approved