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A225976 Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.

%I A225976 #8 Sep 05 2018 14:50:54
%S A225976 4,15,48,138,350,790,1616,3049,5384,9001,14376,22092,32850,47480,
%T A225976 66952,92387,125068,166451,218176,282078,360198,454794,568352,703597,
%U A225976 863504,1051309,1270520,1524928,1818618,2155980,2541720,2980871,3478804,4041239
%N A225976 Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order.
%H A225976 R. H. Hardin, <a href="/A225976/b225976.txt">Table of n, a(n) for n = 1..210</a>
%F A225976 Empirical: a(n) = (11/120)*n^5 - (1/8)*n^4 + (9/8)*n^3 - (7/8)*n^2 + (287/60)*n - 1.
%F A225976 Conjectures from _Colin Barker_, Sep 05 2018: (Start)
%F A225976 G.f.: x*(4 - 9*x + 18*x^2 - 5*x^3 + 2*x^4 + x^5) / (1 - x)^6.
%F A225976 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A225976 (End)
%e A225976 Some solutions for n=3:
%e A225976 ..0..1....1..1....0..0....0..0....1..1....0..1....0..0....0..1....1..1....0..1
%e A225976 ..0..0....1..1....1..1....0..1....1..0....0..1....0..1....0..1....0..0....0..1
%e A225976 ..1..1....0..1....0..0....1..1....1..0....0..1....0..0....1..0....1..1....1..1
%Y A225976 Column 2 of A225982.
%K A225976 nonn
%O A225976 1,1
%A A225976 _R. H. Hardin_, May 22 2013