A250585 - OEIS

%I #7 Nov 15 2018 08:38:14

%S 40,167,639,2375,8625,30952,110187,390391,1378890,4860979,17115235,

%T 60214730,211741401,744338632,2616055529,9193203944,32303585679,

%U 113504084395,398802149195,1401180399346,4922940442496,17296221980468

%N Number of (n+1) X (1+1) 0..2 arrays with nondecreasing max(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 R. H. Hardin, <a href="/A250585/b250585.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 12*a(n-3) + 21*a(n-4) + 3*a(n-5) - 15*a(n-6) + 3*a(n-7) + 3*a(n-8) - a(n-9).

%F Empirical g.f.: x*(40 - 73*x - 83*x^2 + 190*x^3 + 12*x^4 - 132*x^5 + 30*x^6 + 26*x^7 - 9*x^8) / ((1 - x)*(1 - 2*x - x^2 + x^3)*(1 - 3*x - 3*x^2 + 4*x^3 + x^4 - x^5)). - _Colin Barker_, Nov 15 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Column 1 of A250592.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2014