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A223576 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)