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A250813 Number of (1+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 A250813 #8 Nov 21 2018 06:13:47
%S A250813 36,100,225,441,784,1296,2025,3025,4356,6084,8281,11025,14400,18496,
%T A250813 23409,29241,36100,44100,53361,64009,76176,90000,105625,123201,142884,
%U A250813 164836,189225,216225,246016,278784,314721,354025,396900,443556,494209
%N A250813 Number of (1+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 A250813 R. H. Hardin, <a href="/A250813/b250813.txt">Table of n, a(n) for n = 1..210</a>
%F A250813 Empirical: a(n) = (1/4)*n^4 + (5/2)*n^3 + (37/4)*n^2 + 15*n + 9.
%F A250813 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250813 G.f.: x*(36 - 80*x + 85*x^2 - 44*x^3 + 9*x^4) / (1 - x)^5.
%F A250813 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 A250813 (End)
%e A250813 Some solutions for n=4:
%e A250813 ..1..2..2..2..2....1..0..1..1..1....1..1..1..1..2....2..0..0..0..0
%e A250813 ..0..2..2..2..2....0..0..1..2..2....0..0..1..1..2....0..0..0..1..2
%Y A250813 Row 1 of A250812.
%K A250813 nonn
%O A250813 1,1
%A A250813 _R. H. Hardin_, Nov 27 2014