A250770 - OEIS

A250770

Number of (2+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 #11 Nov 19 2018 07:18:47

%S 18,34,62,114,214,410,798,1570,3110,6186,12334,24626,49206,98362,

%T 196670,393282,786502,1572938,3145806,6291538,12582998,25165914,

%U 50331742,100663394,201326694,402653290,805306478,1610612850,3221225590

%N Number of (2+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="/A250770/b250770.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(n) = 12*2^(n-1) + 4*n + 2.

%F Empirical g.f.: 2*x*(9 - 19*x + 8*x^2) / ((1 - x)^2*(1 - 2*x)). - _Colin Barker_, Nov 19 2018

%e Some solutions for n=4:

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

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

%Y Row 2 of A250769.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2014