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A225977 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

%I A225977 #7 Sep 05 2018 14:32:13
%S A225977 8,48,252,1178,4722,16361,49811,135672,336189,768900,1642668,3310404,
%T A225977 6343682,11635425,20537903,35044430,58024377,93522432,147134436,
%U A225977 226473606,341742522,506427905,738136947,1059595772,1499832509
%N A225977 Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.
%H A225977 R. H. Hardin, <a href="/A225977/b225977.txt">Table of n, a(n) for n = 1..101</a>
%F A225977 Empirical: a(n) = (1/4320)*n^9 + (23/6720)*n^8 + (5/336)*n^7 - (1/288)*n^6 + (659/1440)*n^5 + (443/2880)*n^4 + (80/27)*n^3 - (6203/1008)*n^2 + (2459/140)*n - 6 for n>1.
%F A225977 Conjectures from _Colin Barker_, Sep 05 2018: (Start)
%F A225977 G.f.: x*(8 - 32*x + 132*x^2 - 142*x^3 + 202*x^4 - 25*x^5 - 165*x^6 + 163*x^7 - 72*x^8 + 16*x^9 - x^10) / (1 - x)^10.
%F A225977 a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.
%F A225977 (End)
%e A225977 Some solutions for n=3:
%e A225977 ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..1....0..1..1
%e A225977 ..1..0..0....0..1..0....1..1..1....1..0..1....0..1..0....0..1..0....0..0..1
%e A225977 ..1..1..1....0..1..1....0..1..0....0..0..1....0..0..1....0..1..1....1..0..0
%Y A225977 Column 3 of A225982.
%K A225977 nonn
%O A225977 1,1
%A A225977 _R. H. Hardin_, May 22 2013