A250851 - OEIS

A250851

Number of (n+1) X (6+1) 0..3 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 #8 Nov 21 2018 11:26:50

%S 14400,103293,614965,3204951,15344785,69543783,303858745,1294875471,

%T 5422612945,22429374423,91953454825,374560079391,1518555885505,

%U 6135323831463,24724903375705,99451052025711,399459752428465

%N Number of (n+1) X (6+1) 0..3 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="/A250851/b250851.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (282492*4^n - 462196*3^n + 224994*2^n - 20568)/12.

%F Empirical g.f.: x*(14400 - 40707*x + 86035*x^2 - 49444*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 21 2018

%e Some solutions for n=2:

%e ..1..1..0..1..1..1..1....3..3..2..3..3..3..3....3..3..2..2..1..1..1

%e ..0..0..0..1..2..3..3....0..0..1..2..2..2..2....0..0..0..0..0..0..0

%e ..0..0..0..1..2..3..3....0..0..1..2..2..3..3....1..1..1..1..3..3..3

%Y Column 6 of A250853.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014