A163684 Number of n X n binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent.

1, 3, 17, 132, 1561, 27874, 809249, 41309900, 3719895992, 564046444356, 139282673506635, 55729534542527798, 36581083479684327514, 40002510692269168858899, 73613357474514877939445116

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

All solutions for n=3:
...1.0.0...1.0.0...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...1.1.1...1.1.0
...1.1.0...1.1.1...1.0.0...1.0.1...1.0.0...1.0.1...1.0.0...1.0.1...0.1.0
...0.1.1...0.0.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1
------
...1.1.0...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.0.1...1.1.1
...0.1.1...0.0.1...0.0.1...1.0.1...1.0.1...1.0.1...1.0.1...0.0.1
...0.0.1...0.0.1...0.1.1...0.0.1...0.1.1...1.0.1...1.1.1...1.1.1

Crossrefs

Main diagonal of A391818.

Sequence in context: A392203 A307680 A305819 * A363135 A093986 A192459

Adjacent sequences: A163681 A163682 A163683 * A163685 A163686 A163687

Keyword

nonn

Author

R. H. Hardin, Aug 03 2009

Extensions

a(8)-a(15) from Andrew Howroyd, Dec 22 2025

Status

approved