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A250814 Number of (2+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 A250814 #8 Nov 21 2018 06:13:53
%S A250814 129,379,873,1731,3097,5139,8049,12043,17361,24267,33049,44019,57513,
%T A250814 73891,93537,116859,144289,176283,213321,255907,304569,359859,422353,
%U A250814 492651,571377,659179,756729,864723,983881,1114947,1258689,1415899
%N A250814 Number of (2+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 A250814 R. H. Hardin, <a href="/A250814/b250814.txt">Table of n, a(n) for n = 1..210</a>
%F A250814 Empirical: a(n) = 1*n^4 + 10*n^3 + 37*n^2 + 54*n + 27.
%F A250814 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250814 G.f.: x*(129 - 266*x + 268*x^2 - 134*x^3 + 27*x^4) / (1 - x)^5.
%F A250814 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 A250814 (End)
%e A250814 Some solutions for n=4:
%e A250814 ..1..1..1..0..0....2..2..1..1..1....1..1..0..0..0....2..1..1..1..1
%e A250814 ..0..0..0..1..1....0..1..1..1..1....0..0..0..2..2....1..1..2..2..2
%e A250814 ..0..0..1..2..2....0..1..1..1..2....0..0..0..2..2....0..0..1..2..2
%Y A250814 Row 2 of A250812.
%K A250814 nonn
%O A250814 1,1
%A A250814 _R. H. Hardin_, Nov 27 2014