A250777 - OEIS

A250777

Number of (n+1) X (2+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 09:13:56

%S 21,46,96,196,396,796,1596,3196,6396,12796,25596,51196,102396,204796,

%T 409596,819196,1638396,3276796,6553596,13107196,26214396,52428796,

%U 104857596,209715196,419430396,838860796,1677721596,3355443196

%N Number of (n+1) X (2+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="/A250777/b250777.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2); a(n) = 25*2^(n-1) - 4.

%F Empirical g.f.: x*(21 - 17*x) / ((1 - x)*(1 - 2*x)). - _Colin Barker_, Nov 19 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A250783.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014