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A266937 Number of 4 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.

%I A266937 #8 Jan 10 2019 10:23:54
%S A266937 5,12,20,35,52,82,115,169,232,322,426,573,738,961,1215,1543,1912,2382,
%T A266937 2905,3557,4280,5161,6135,7308,8594,10120,11791,13749,15883,18361,
%U A266937 21049,24142,27490,31307,35427,40093,45111,50757,56818,63594,70848,78917,87535
%N A266937 Number of 4 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
%H A266937 R. H. Hardin, <a href="/A266937/b266937.txt">Table of n, a(n) for n = 1..87</a>
%F A266937 Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) - a(n-5) - a(n-6) + 2*a(n-8) + 2*a(n-9) - a(n-11) - a(n-12) - a(n-13) - a(n-14) + 2*a(n-15) + a(n-16) -a(n-17).
%F A266937 Empirical g.f.: x*(5 + 7*x - 2*x^2 - 4*x^3 - 6*x^4 - 3*x^5 + x^6 + 9*x^7 + 12*x^8 + 2*x^9 -6*x^10 - 4*x^11 - 6*x^12 - 5*x^13 + 9*x^14 + 6*x^15 - 5*x^16) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Jan 10 2019
%e A266937 Some solutions for n=4:
%e A266937 ..0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..1
%e A266937 ..1..1..0..1....0..0..1..0....1..1..0..1....0..0..0..0....0..0..1..1
%e A266937 ..1..1..1..0....1..1..0..0....1..1..1..0....1..1..1..1....1..1..0..0
%e A266937 ..1..1..1..0....1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0
%Y A266937 Row 4 of A266935.
%K A266937 nonn
%O A266937 1,1
%A A266937 _R. H. Hardin_, Jan 06 2016