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%I #7 Nov 22 2018 14:28:45
%S 37130,131068,317878,629528,1097986,1755220,2633198,3763888,5179258,
%T 6911276,8991910,11453128,14326898,17645188,21439966,25743200,
%U 30586858,36002908,42023318,48680056,56005090,64030388,72787918,82309648,92627546
%N Number of (5+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
%H R. H. Hardin, <a href="/A250882/b250882.txt">Table of n, a(n) for n = 1..156</a>
%F Empirical: a(n) = 5328*n^3 + 14468*n^2 + 13238*n + 4096.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: 2*x*(18565 - 8726*x + 8193*x^2 - 2048*x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=2:
%e ..1..1..1....2..2..2....1..1..1....2..2..2....0..0..1....2..3..3....0..0..0
%e ..2..2..2....0..0..0....1..1..1....3..3..3....1..1..2....1..2..3....2..3..3
%e ..1..1..1....3..3..3....2..2..2....1..1..2....2..2..3....1..2..3....0..1..1
%e ..3..3..3....2..2..2....2..2..2....0..0..2....0..1..2....1..2..3....2..3..3
%e ..2..2..2....0..1..1....3..3..3....1..1..3....1..2..3....0..2..3....1..3..3
%e ..0..1..2....0..2..3....2..3..3....0..0..2....0..1..2....0..2..3....1..3..3
%Y Row 5 of A250877.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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