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A266542 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

%I A266542 #8 Jan 10 2019 08:09:26
%S A266542 2,3,5,6,8,11,13,16,20,23,27,32,36,41,47,52,58,65,71,78,86,93,101,110,
%T A266542 118,127,137,146,156,167,177,188,200,211,223,236,248,261,275,288,302,
%U A266542 317,331,346,362,377,393,410,426,443,461,478,496,515,533,552,572,591,611,632
%N A266542 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.
%H A266542 R. H. Hardin, <a href="/A266542/b266542.txt">Table of n, a(n) for n = 1..210</a>
%F A266542 Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
%F A266542 Empirical g.f.: x*(2 - x + x^2 - 3*x^3 + 2*x^4) / ((1 - x)^3*(1 + x + x^2)). - _Colin Barker_, Jan 10 2019
%e A266542 Some solutions for n=6:
%e A266542 ..0..1..1....0..1..1....0..0..1....0..1..1....0..1..1....0..1..1....0..0..1
%e A266542 ..0..1..1....1..0..1....0..1..0....1..0..0....0..1..1....0..1..1....0..0..1
%e A266542 ..1..0..1....1..1..0....0..1..0....1..0..0....0..1..1....1..0..0....0..1..0
%e A266542 ..1..0..1....1..1..0....1..0..0....1..0..0....1..0..0....1..0..0....0..1..0
%e A266542 ..1..1..0....1..1..0....1..0..0....1..0..0....1..0..0....1..0..0....1..0..0
%e A266542 ..1..1..0....1..1..0....1..0..0....1..0..0....1..0..0....1..0..0....1..0..0
%Y A266542 Column 3 of A266547.
%K A266542 nonn
%O A266542 1,1
%A A266542 _R. H. Hardin_, Dec 31 2015