A223569 T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal

2, 4, 4, 8, 16, 8, 16, 64, 64, 16, 32, 256, 448, 256, 32, 64, 1024, 3136, 3136, 1024, 64, 128, 4096, 21952, 34496, 21952, 4096, 128, 256, 16384, 153664, 379456, 379456, 153664, 16384, 256, 512, 65536, 1075648, 4174016, 6071296, 4174016, 1075648

Offset

1,1

Comments

Table starts

....2.......4.........8..........16............32..............64

....4......16........64.........256..........1024............4096

....8......64.......448........3136.........21952..........153664

...16.....256......3136.......34496........379456.........4174016

...32....1024.....21952......379456.......6071296........97140736

...64....4096....153664.....4174016......97140736......2137096192

..128...16384...1075648....45914176....1554251776.....47016116224

..256...65536...7529536...505055936...24868028416...1034354556928

..512..262144..52706752..5555615296..397888454656..22755800252416

.1024.1048576.368947264.61111768256.6366215274496.500627605553152

Links

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

Formula

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

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A000302

Sequence in context: A188910 A189111 A181217 * A227594 A321241 A290128

Adjacent sequences: A223566 A223567 A223568 * A223570 A223571 A223572

Keyword

nonn,tabl

Author

R. H. Hardin Mar 22 2013

Status

approved