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

1,1

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

Links

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

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

Example

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

Crossrefs

Cf. A304387.

Sequence in context: A019547 A228878 A067673 * A045253 A088868 A373734

Adjacent sequences: A250650 A250651 A250652 * A250654 A250655 A250656

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved