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%I #8 Jan 10 2019 08:08:52
%S 2,5,12,29,67,147,303,590,1090,1922,3253,5311,8400,12918,19377,28425,
%T 40873,57722,80196,109776,148240,197703,260666,340063,439318,562401,
%U 713894,899055,1123895,1395251,1720873,2109508,2570998,3116374,3757967
%N Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%H R. H. Hardin, <a href="/A266465/b266465.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + a(n-3) + 9*a(n-4) - 6*a(n-5) - 6*a(n-7) + 9*a(n-8) + a(n-9) - 8*a(n-10) + 5*a(n-11) - a(n-12).
%F Empirical g.f.: x*(2 - 5*x + 3*x^2 + 7*x^3 - 5*x^4 - x^5 - 3*x^6 + 7*x^7 - 7*x^9 + 5*x^10 - x^11) / ((1 - x)^8*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jan 10 2019
%e Some solutions for n=4:
%e ..0..0..0....0..0..0....0..1..1....0..1..1....0..0..1....0..0..1....0..0..1
%e ..0..0..0....0..1..1....1..0..1....1..0..1....0..1..0....1..1..0....0..1..0
%e ..0..0..0....1..0..0....1..1..0....1..1..0....1..0..0....1..1..1....1..0..0
%e ..0..0..0....1..1..1....1..1..0....1..1..1....1..1..0....1..1..1....1..1..1
%Y Column 3 of A266470.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2015
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