A223585 T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal

4, 16, 16, 64, 256, 64, 256, 4096, 4096, 256, 1024, 65536, 204800, 65536, 1024, 4096, 1048576, 10240000, 10240000, 1048576, 4096, 16384, 16777216, 512000000, 1331200000, 512000000, 16777216, 16384, 65536, 268435456, 25600000000

Offset

1,1

Comments

Table starts

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

....16........256...........4096..............65536................1048576

....64.......4096.........204800...........10240000..............512000000

...256......65536.......10240000.........1331200000...........173056000000

..1024....1048576......512000000.......173056000000.........51224576000000

..4096...16777216....25600000000.....22497280000000......15162474496000000

.16384..268435456..1280000000000...2924646400000000....4488092450816000000

.65536.4294967296.64000000000000.380204032000000000.1328475365441536000000

Links

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

Formula

Let U(z) = (z^6+15*z^5+115*z^4+405*z^3+964*z^2+660*z+720)/720

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..0..1..1....0..0..3..3....0..0..0..3....0..0..0..0....0..0..3..2
..0..2..2..2....0..3..2..2....0..2..3..2....0..3..1..1....0..1..0..2
..0..2..3..3....1..1..0..2....0..2..0..0....1..1..1..3....0..0..0..0

Crossrefs

Column 1 is A000302

Column 2 is A001025

Sequence in context: A267974 A267997 A229105 * A202680 A263568 A009570

Adjacent sequences: A223582 A223583 A223584 * A223586 A223587 A223588

Keyword

nonn,tabl

Author

R. H. Hardin Mar 22 2013

Status

approved