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T(n,k)=Number of (n+1)X(k+1) 0..3 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
9

%I #5 Mar 31 2012 12:36:58

%S 90,565,565,3352,10109,3352,18332,187118,187118,18332,93578,2903185,

%T 13948153,2903185,93578,452825,38244007,855879499,855879499,38244007,

%U 452825,2103364,439011778,42858325343,215433191774,42858325343,439011778

%N T(n,k)=Number of (n+1)X(k+1) 0..3 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 ......90.........565.............3352.................18332

%C .....565.......10109...........187118...............2903185

%C ....3352......187118.........13948153.............855879499

%C ...18332.....2903185........855879499..........215433191774

%C ...93578....38244007......42858325343........43960759831841

%C ..452825...439011778....1799006388496......7419043577516162

%C .2103364..4495376717...65121080193243...1066959581935799954

%C .9466880.41798687510.2076963297883071.133822712331030881445

%H R. H. Hardin, <a href="/A203787/b203787.txt">Table of n, a(n) for n = 1..71</a>

%e Some solutions for n=4 k=3

%e ..0..1..1..3....2..0..0..2....3..0..1..1....3..0..0..2....1..0..0..0

%e ..1..2..2..0....1..3..3..2....0..3..2..2....0..3..3..2....0..3..3..3

%e ..3..1..1..3....3..2..3..1....3..2..3..3....0..3..3..2....1..3..3..3

%e ..2..2..3..1....2..3..2..2....2..3..3..3....3..1..1..3....3..3..3..3

%e ..2..3..0..2....2..3..2..2....2..3..3..3....2..2..2..2....3..3..3..3

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 05 2012