A250987 - OEIS

%I #8 Nov 24 2018 08:12:02

%S 40,158,612,2323,8726,32554,120930,447985,1656600,6118822,22583412,

%T 83309947,307230262,1132763986,4175945922,15393274457,56738968328,

%U 209129360814,770792626564,2840879847779,10470404185174,38589657774202

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

%H R. H. Hardin, <a href="/A250987/b250987.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(40 - 82*x - 56*x^2 + 77*x^3 + 56*x^4 + 9*x^5) / ((1 - 2*x - x^2)*(1 - 4*x + 4*x^3 + x^4)). - _Colin Barker_, Nov 24 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A250994.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2014