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A201371 Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

%I A201371 #8 May 22 2018 20:37:13
%S A201371 2,5,14,36,80,157,280,464,726,1085,1562,2180,2964,3941,5140,6592,8330,
%T A201371 10389,12806,15620,18872,22605,26864,31696,37150,43277,50130,57764,
%U A201371 66236,75605,85932,97280,109714,123301,138110,154212,171680,190589,211016
%N A201371 Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
%C A201371 Column 4 of A201375.
%H A201371 R. H. Hardin, <a href="/A201371/b201371.txt">Table of n, a(n) for n = 1..210</a>
%F A201371 Empirical: a(n) = (1/12)*n^4 + (1/3)*n^3 - (13/12)*n^2 + (8/3)*n.
%F A201371 Conjectures from _Colin Barker_, May 22 2018: (Start)
%F A201371 G.f.: x*(2 - 5*x + 9*x^2 - 4*x^3) / (1 - x)^5.
%F A201371 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A201371 (End)
%e A201371 Some solutions for n=5:
%e A201371 ..0..0..1..1....0..0..1..1....0..1..1..1....0..1..1..1....0..0..0..1
%e A201371 ..0..0..1..1....0..0..1..1....1..0..1..1....0..1..1..1....0..0..0..1
%e A201371 ..1..1..0..1....0..1..0..1....1..1..0..0....1..0..0..1....0..0..0..1
%e A201371 ..1..1..1..0....0..1..1..0....1..1..0..0....1..1..1..0....0..0..1..0
%e A201371 ..1..1..1..0....1..0..0..0....1..1..0..0....1..1..1..0....1..1..0..0
%Y A201371 Cf. A201375.
%K A201371 nonn
%O A201371 1,1
%A A201371 _R. H. Hardin_, Nov 30 2011