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A184138 Number of n X 3 binary arrays with rows and columns in nondecreasing order.

%I A184138 #10 Apr 12 2018 06:31:59
%S A184138 4,14,45,130,336,785,1682,3351,6280,11176,19031,31200,49492,76275,
%T A184138 114596,168317,242268,342418,476065,652046,880968,1175461,1550454,
%U A184138 2023475,2614976,3348684,4251979,5356300,6697580,8316711,10260040,12579897
%N A184138 Number of n X 3 binary arrays with rows and columns in nondecreasing order.
%C A184138 Column 3 of A180985.
%H A184138 R. H. Hardin, <a href="/A184138/b184138.txt">Table of n, a(n) for n = 1..200</a>
%F A184138 Empirical: a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) (=polynomial degree 7).
%F A184138 Conjectures from _Colin Barker_, Apr 12 2018: (Start)
%F A184138 G.f.: x*(4 - 18*x + 45*x^2 - 62*x^3 + 52*x^4 - 27*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A184138 a(n) = (5040 + 7860*n + 4494*n^2 + 2044*n^3 + 525*n^4 + 175*n^5 + 21*n^6 + n^7) / 5040.
%F A184138 (End)
%e A184138 Some solutions for 5 X 3:
%e A184138 ..0..0..0....0..0..0....0..0..0....0..0..1....0..1..1....0..0..0....0..0..0
%e A184138 ..0..0..1....0..0..1....0..0..0....0..1..0....0..1..1....0..1..1....0..0..1
%e A184138 ..1..1..0....1..1..1....0..0..0....0..1..0....1..0..1....0..1..1....0..1..1
%e A184138 ..1..1..0....1..1..1....0..0..1....0..1..1....1..0..1....0..1..1....1..1..0
%e A184138 ..1..1..0....1..1..1....1..1..1....1..0..1....1..1..1....0..1..1....1..1..1
%Y A184138 Cf. A180985.
%K A184138 nonn
%O A184138 1,1
%A A184138 _R. H. Hardin_, Jan 09 2011