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%I #5 Mar 31 2012 12:36:57
%S 8,16,16,32,34,32,64,80,80,64,128,174,321,174,128,256,376,1177,1177,
%T 376,256,512,786,4200,7481,4200,786,512,1024,1624,13777,46853,46853,
%U 13777,1624,1024,2048,3310,42112,265581,554620,265581,42112,3310,2048,4096
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
%C Table starts
%C ....8...16.....32......64.......128.........256...........512............1024
%C ...16...34.....80.....174.......376.........786..........1624............3310
%C ...32...80....321....1177......4200.......13777.........42112..........120522
%C ...64..174...1177....7481.....46853......265581.......1371532.........6477799
%C ..128..376...4200...46853....554620.....5972476......58336803.......513856445
%C ..256..786..13777..265581...5972476...125140148....2396938985.....41222650083
%C ..512.1624..42112.1371532..58336803..2396938985...91479447926...3140066953229
%C .1024.3310.120522.6477799.513856445.41222650083.3140066953229.216607480473481
%H R. H. Hardin, <a href="/A203452/b203452.txt">Table of n, a(n) for n = 1..220</a>
%e Some solutions for n=7 k=3
%e ..0..1..0..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..0..0
%e ..1..0..1..1....0..0..0..1....0..1..0..1....0..1..0..1....0..0..0..1
%e ..0..1..1..0....0..0..1..0....1..0..1..0....1..0..1..0....0..0..1..1
%e ..0..1..1..0....0..1..0..1....1..0..1..1....1..0..1..0....0..1..0..0
%e ..0..1..1..0....1..0..1..1....1..0..1..1....0..1..1..0....1..0..1..0
%e ..1..1..0..0....0..1..1..0....0..1..1..0....1..1..0..1....1..0..1..0
%e ..1..1..0..0....1..1..0..0....1..1..0..0....1..1..1..1....1..0..1..1
%e ..1..1..1..1....1..1..1..0....1..1..0..1....1..1..1..1....0..1..1..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 02 2012
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