A227061 - OEIS

%I #9 Sep 12 2019 19:27:35

%S 1,1,1,1,1,1,1,1,2,1,1,1,3,5,1,1,1,5,25,13,1,1,1,8,161,272,42,1,1,1,

%T 13,1112,7776,4070,155,1,1,1,21,8787,287311,626649,79221,636,1,1,1,34,

%U 76156,13704640,137393147,70821384,1906501,2889,1,1,1,55,728699,809171699

%N T(n,k) = Number of (n+k-1) X (n+k-1) binary arrays with k 1s in every row and column with rows and columns in lexicographically nondecreasing order.

%C Table starts

%C .1...1.....1......1......1....1.....1..1.1.1

%C .1...1.....1......1......1....1.....1..1.1

%C .1...2.....3......5......8...13....21.34

%C .1...5....25....161...1112.8787.76156

%C .1..13...272...7776.287311

%C .1..42..4070.626649

%C .1.155.79221

%C .1.636

%e Some solutions for n=4 k=4

%e ..0..0..0..1..1..1..1....0..0..0..1..1..1..1....0..0..0..1..1..1..1

%e ..0..1..1..0..0..1..1....0..1..1..0..0..1..1....0..0..0..1..1..1..1

%e ..0..1..1..0..1..0..1....0..1..1..0..1..0..1....0..1..1..0..0..1..1

%e ..1..0..0..1..0..1..1....1..0..0..1..1..1..0....1..0..0..1..1..0..1

%e ..1..0..1..1..1..0..0....1..0..1..0..0..1..1....1..1..1..0..0..1..0

%e ..1..1..0..1..0..1..0....1..1..0..1..1..0..0....1..1..1..0..1..0..0

%e ..1..1..1..0..1..0..0....1..1..1..1..0..0..0....1..1..1..1..0..0..0

%Y Column 2 is A229161(n+1).

%Y Column 3 is A229162(n+2).

%Y Column 4 is A229163(n+3).

%Y Column 5 is A229164(n+4).

%Y Row 3 is A000045(n+1).

%Y Row 4 is A181344(n+3).

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_ Sep 17 2013

%E More terms from _Sean A. Irvine_, Sep 12 2019