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%I #15 Jun 17 2017 03:06:05
%S 8,64,216,528,1080,1968,3304,5216,7848,11360,15928,21744,29016,37968,
%T 48840,61888,77384,95616,116888,141520,169848,202224,239016,280608,
%U 327400,379808,438264,503216,575128,654480,741768,837504,942216,1056448
%N Number of 4 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
%H Don Coppersmith, <a href="http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/March2004.html">Ponder This: IBM Research Monthly Puzzles, March challenge</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 2/3*n*(n^3+6*n^2+11*n-6). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m-1, n)-m) = 4/Beta(m, n)-2*m*n.
%F G.f.: -8*x*(x^3-3*x^2+3*x+1) / (x-1)^5. [_Colin Barker_, Feb 22 2013]
%Y Cf. A032260, A016742, A086113, A086115.
%K nonn,easy
%O 1,1
%A _Vladimir Baltic_, _Vladeta Jovovic_, Jul 10 2003
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