A171699 Square array of number of distinct m X n (0,1) matrices after iterated double sorting, read by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 14, 14, 5, 1, 1, 6, 25, 45, 25, 6, 1, 1, 7, 41, 130, 130, 41, 7, 1, 1, 8, 63, 336, 650, 336, 63, 8, 1, 1, 9, 92, 785, 2942, 2942, 785, 92, 9, 1, 1, 10, 129, 1682, 11819, 24520, 11819, 1682, 129, 10, 1, 1, 11, 175

Offset

0,5

Comments

T(m,n) gives the number of distinct results obtained by repeatedly sorting the m X n (0,1) matrices by columns & then rows until reaching a fixed point. Its diagonal is A089006.

Links

Table of n, a(n) for n=0..68.

Example

Array begins:
  1,1,1,1,1,...
  1,2,3,4,5,...
  1,3,7,14,25,...
  1,4,14,45,130,...
  1,5,25,130,650,...

Prog

(Haskell)
-- with the function "t" producing the array.
import List
prod = foldr (\x xs -> [y:ys | y <- x, ys <- xs]) [[]]
f xs = let ys = sort (transpose (sort (transpose xs))) in if xs == ys then xs else f ys
t m n = length $ nub $ map f $ prod (replicate m (prod (replicate n [0, 1])))

Crossrefs

Cf. A089006.

Sequence in context: A028657 A053534 A104881 * A104878 A196863 A196922

Adjacent sequences: A171696 A171697 A171698 * A171700 A171701 A171702

Keyword

nonn,tabl

Author

Randy Compton (RANDYRulerOfZexernet(AT)gmail.com), Dec 15 2009

Extensions

Corrected & extended by Randy Compton (RANDYRulerOfZexernet(AT)gmail.com), Dec 18 2009

Status

approved