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%I #9 Jan 09 2019 14:23:52
%S 4,13,35,82,173,337,614,1060,1749,2777,4266,6369,9273,13206,18441,
%T 25302,34170,45490,59776,77620,99698,126778,159728,199525,247262,
%U 304159,371571,450998,544095,652683,778758,924504,1092303,1284747,1504650,1755061
%N Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nondecreasing.
%H R. H. Hardin, <a href="/A266357/b266357.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 5*a(n-1) -9*a(n-2) +6*a(n-3) -6*a(n-7) +9*a(n-8) -5*a(n-9) +a(n-10).
%F Empirical g.f.: x*(4 - 7*x + 6*x^2 - 6*x^6 + 9*x^7 - 5*x^8 + x^9) / ((1 - x)^7*(1 + x)*(1 + x + x^2)). - _Colin Barker_, Jan 09 2019
%e Some solutions for n=4:
%e ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..0
%e ..0..0..1....0..0..1....0..1..1....0..1..0....0..1..1....0..0..1....0..0..0
%e ..0..1..0....0..1..1....1..1..1....0..1..0....1..0..1....0..0..1....0..1..1
%e ..1..0..1....1..1..0....1..1..1....1..0..1....1..1..1....0..1..1....1..1..1
%Y Column 3 of A266362.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 28 2015