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A266423 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

%I A266423 #9 Jan 09 2019 14:45:16
%S A266423 4,14,39,96,212,433,826,1493,2575,4270,6841,10639,16114,23845,34555,
%T A266423 49147,68725,94637,128501,172257,228199,299035,387927,498560,635189,
%U A266423 802719,1006760,1253717,1550855,1906400,2329613,2830904,3421916,4115651
%N A266423 Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
%H A266423 R. H. Hardin, <a href="/A266423/b266423.txt">Table of n, a(n) for n = 1..200</a>
%F A266423 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 A266423 Empirical g.f.: x*(4 - 6*x + x^2 + 9*x^3 - 6*x^4 - 6*x^6 + 9*x^7 + x^8 - 8*x^9 + 5*x^10 - x^11) / ((1 - x)^8*(1 + x)^2*(1 + x + x^2)). - _Colin Barker_, Jan 09 2019
%e A266423 Some solutions for n=4:
%e A266423 ..0..0..1....0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..1
%e A266423 ..0..0..1....0..1..1....0..0..0....0..0..1....0..1..1....0..0..0....0..1..1
%e A266423 ..1..1..0....1..1..0....0..0..1....0..1..1....0..1..1....0..0..0....1..1..1
%e A266423 ..1..1..0....1..1..1....1..1..1....0..1..1....0..1..1....1..1..1....1..1..1
%Y A266423 Column 3 of A266428.
%K A266423 nonn
%O A266423 1,1
%A A266423 _R. H. Hardin_, Dec 29 2015