A202882 Number of n X 1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

1, 3, 9, 22, 51, 121, 292, 704, 1691, 4059, 9749, 23422, 56268, 135166, 324692, 779977, 1873673, 4500958, 10812237, 25973244, 62393157, 149881402, 360046432, 864906711, 2077686532, 4991036946, 11989513056, 28801314179, 69186771332

Offset

1,2

Links

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

T. Mansour and M. Shattuck, Counting Peaks and Valleys in a Partition of a Set, J. Int. Seq. 13 (2010), 10.6.8, Lemma 2.1, k=3, one peak.

Formula

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5).

Empirical: G.f.: -x*(1+3*x^2+x^4)/(-1+3*x-3*x^2+4*x^3-x^4+x^5). - R. J. Mathar, Jul 09 2017

Example

Some solutions for n=5
..2....2....1....0....2....2....0....1....0....1....1....0....2....1....0....2
..2....2....1....1....2....2....2....1....2....2....1....0....2....2....1....2
..0....1....1....2....0....2....2....0....2....2....1....1....1....2....1....0
..0....1....1....2....1....1....2....0....0....0....2....1....2....2....2....2
..0....0....1....2....1....1....1....0....0....0....2....1....2....0....2....2

Crossrefs

Column 1 of A202889.

Sequence in context: A099166 A222083 A305612 * A350105 A336511 A054442

Adjacent sequences: A202879 A202880 A202881 * A202883 A202884 A202885

Keyword

nonn

Author

R. H. Hardin, Dec 25 2011

Status

approved