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A223585 T(n,k)=Number of nXk 0..3 arrays with antidiagonals unimodal 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)