A250653 Number of (n+1)X(5+1) 0..1 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.

49, 103, 211, 427, 859, 1723, 3451, 6907, 13819, 27643, 55291, 110587, 221179, 442363, 884731, 1769467, 3538939, 7077883, 14155771, 28311547, 56623099, 113246203, 226492411, 452984827, 905969659, 1811939323, 3623878651

Offset: 1

Author

R. H. Hardin, Nov 26 2014

Keywords

• nonn

Comments

Column 5 of A250656.

Since one edge length of the array is fixed, and the constraint is a Markov-type correlation between fixed-width lengths of the other edge, the generating function is computable by the usual transfer matrix method and therefore a rational polynomial. That predicts that there is a linear recurrence. - R. J. Mathar, May 25 2018

Examples

			Some solutions for n=4
..1..1..1..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..0..0
..0..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....0..0..0..0..0..0
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
..0..0..0..0..1..1....1..1..1..1..1..1....0..0..0..0..1..1....0..0..0..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A304387.

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*25 + (5*2^(n-1)-1)*5 + 2^(n+1).

It appears that a(n) = 27*2^n-5, which would make this coincide with A304387. - N. J. A. Sloane, May 13 2018