A203094 Number of nX1 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

1, 4, 16, 50, 144, 422, 1268, 3823, 11472, 34350, 102896, 308419, 924532, 2771101, 8305373, 24892609, 74608516, 223618304, 670231838, 2008825312, 6020872062, 18045827096, 54087163859, 162110668160, 485879938474, 1456284886944

Offset: 1

Author

R. H. Hardin, Dec 29 2011

Keywords

• nonn

Examples

			Some solutions for n=5
..3....1....1....1....1....3....3....1....0....1....1....3....2....0....3....3
..3....1....1....2....2....3....3....1....2....1....1....3....2....2....3....3
..1....3....1....2....3....3....1....0....3....0....2....3....3....3....3....0
..3....3....2....1....3....3....3....0....3....0....2....3....3....3....2....1
..3....0....2....0....3....0....3....0....0....0....1....0....1....3....1....1
		

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=4, no peak.

Crossrefs

Column 1 of A203101. Also a column of A228461. Cf. A217883, A217954.

Formula

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7).

Empirical: G.f.: -x*(1+6*x^2+5*x^4+x^6) / (-1+4*x-6*x^2+10*x^3-5*x^4+6*x^5-x^6+x^7). - R. J. Mathar, May 17 2014