A250771 - OEIS

A250771

Number of (3+1) X (n+1) 0..1 arrays with nondecreasing 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.

%I #8 Nov 19 2018 07:18:54

%S 36,66,114,196,344,622,1158,2208,4284,8410,16634,33052,65856,131430,

%T 262542,524728,1049060,2097682,4194882,8389236,16777896,33555166,

%U 67109654,134218576,268436364,536871882,1073742858,2147484748,4294968464

%N Number of (3+1) X (n+1) 0..1 arrays with nondecreasing 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="/A250771/b250771.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(n) = 16*2^(n-1) + n^2 + 11*n + 8.

%F Empirical g.f.: 2*x*(3 - 2*x)*(6 - 15*x + 8*x^2) / ((1 - x)^3*(1 - 2*x)). - _Colin Barker_, Nov 19 2018

%e Some solutions for n=4:

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

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

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

%Y Row 3 of A250769.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014