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%I #13 Mar 17 2024 11:13:05
%S 4,13,42,141,486,1685,5804,19769,66544,221581,730918,2391717,7772610,
%T 25110933,80713016,258280817,823269116,2615088973,8281113730,
%U 26150883901,82375282494,258893742933,811984918692,2541865829801,7943330715176
%N Number of n X 3 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.
%H R. H. Hardin, <a href="/A267240/b267240.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A267240/a267240.pdf">Maple-assisted proof of empirical recurrence</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10, -39, 76, -79, 42, -9).
%F Empirical: a(n) = 10*a(n-1) - 39*a(n-2) + 76*a(n-3) - 79*a(n-4) + 42*a(n-5) - 9*a(n-6).
%F Conjectures from _Colin Barker_, Jan 11 2019: (Start)
%F G.f.: x*(4 - 27*x + 68*x^2 - 76*x^3 + 42*x^4 - 9*x^5) / ((1 - x)^4*(1 - 3*x)^2).
%F a(n) = (24 + (31+3^(2+n))*n + 12*n^2 + 2*n^3) / 24.
%F (End)
%F Empirical recurrence verified (see link). - _Robert Israel_, Sep 08 2019
%e Some solutions for n=4:
%e ..0..0..1....0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..0..1
%e ..0..1..0....0..1..0....0..1..1....0..0..1....0..1..0....0..0..1....1..1..0
%e ..1..0..0....1..1..0....1..0..1....0..1..1....0..0..1....0..0..1....0..1..1
%e ..1..1..0....1..1..1....0..1..1....0..1..1....0..0..1....1..1..0....1..0..1
%Y Column 3 of A267245.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2016
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