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A250816 Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%I A250816 #8 Nov 21 2018 06:14:07
%S A250816 1389,4321,10233,20631,37333,62469,98481,148123,214461,300873,411049,
%T A250816 548991,719013,925741,1174113,1469379,1817101,2223153,2693721,3235303,
%U A250816 3854709,4559061,5355793,6252651,7257693,8379289,9626121,11007183
%N A250816 Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
%H A250816 R. H. Hardin, <a href="/A250816/b250816.txt">Table of n, a(n) for n = 1..210</a>
%F A250816 Empirical: a(n) = 13*n^4 + 121*n^3 + 439*n^2 + 573*n + 243.
%F A250816 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250816 G.f.: x*(1389 - 2624*x + 2518*x^2 - 1214*x^3 + 243*x^4) / (1 - x)^5.
%F A250816 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 A250816 (End)
%e A250816 Some solutions for n=4:
%e A250816 ..0..0..0..0..0....2..2..1..1..0....2..2..2..1..0....2..2..2..2..1
%e A250816 ..0..0..0..2..2....0..0..0..0..0....0..0..0..0..1....0..0..0..0..0
%e A250816 ..0..0..0..2..2....2..2..2..2..2....0..0..0..1..2....1..1..1..1..1
%e A250816 ..0..0..0..2..2....0..0..1..1..1....0..0..0..1..2....1..1..1..2..2
%e A250816 ..0..0..0..2..2....1..1..2..2..2....0..0..0..1..2....1..1..1..2..2
%Y A250816 Row 4 of A250812.
%K A250816 nonn
%O A250816 1,1
%A A250816 _R. H. Hardin_, Nov 27 2014