A250818 - OEIS

%I #7 Nov 21 2018 08:04:13

%S 13449,42769,102393,207831,377857,634509,1003089,1512163,2193561,

%T 3082377,4216969,5638959,7393233,9527941,12094497,15147579,18745129,

%U 22948353,27821721,33432967,39853089,47156349,55420273,64725651,75156537,86800249

%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 min(x(i,j),x(i-1,j)) in the j direction.

%H R. H. Hardin, <a href="/A250818/b250818.txt">Table of n, a(n) for n = 1..203</a>

%F Empirical: a(n) = 136*n^4 + 1225*n^3 + 4402*n^2 + 5499*n + 2187.

%F Conjectures from _Colin Barker_, Nov 21 2018: (Start)

%F G.f.: x*(13449 - 24476*x + 23038*x^2 - 10934*x^3 + 2187*x^4) / (1 - x)^5.

%F 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 (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

%Y Row 6 of A250812.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014