A250761 - OEIS

%I #8 Nov 18 2018 07:34:48

%S 9585,22197,40023,63063,91317,124785,163467,207363,256473,310797,

%T 370335,435087,505053,580233,660627,746235,837057,933093,1034343,

%U 1140807,1252485,1369377,1491483,1618803,1751337,1889085,2032047,2180223,2333613

%N Number of (6+1) X (n+1) 0..2 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="/A250761/b250761.txt">Table of n, a(n) for n = 1..209</a>

%F Empirical: a(n) = 2607*n^2 + 4791*n + 2187.

%F Conjectures from _Colin Barker_, Nov 18 2018: (Start)

%F G.f.: 3*x*(3195 - 2186*x + 729*x^2) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

%F (End)

%e Some solutions for n=4:

%e ..2..2..2..2..2....0..0..0..0..0....2..2..2..2..2....2..2..2..2..2

%e ..0..0..0..0..0....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0

%e ..2..2..2..2..2....1..1..1..2..2....0..0..0..0..0....2..2..2..2..2

%e ..2..2..2..2..2....0..0..0..1..1....1..1..1..1..1....2..2..2..2..2

%e ..2..2..2..2..2....0..0..0..1..1....2..2..2..2..2....2..2..2..2..2

%e ..1..2..2..2..2....1..1..1..2..2....0..1..1..1..1....1..1..1..1..1

%e ..0..1..1..2..2....1..1..1..2..2....0..2..2..2..2....0..0..0..0..2

%Y Row 6 of A250755.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014