A200866 Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

36, 94, 236, 602, 1528, 3882, 9858, 25038, 63592, 161514, 410218, 1041884, 2646208, 6720920, 17069998, 43354902, 110114102, 279671154, 710317326, 1804085608, 4582071648, 11637685314, 29557748082, 75071670020, 190669317026, 484267746348, 1229957991200, 3123884816870

Offset: 1

Author

R. H. Hardin, Nov 23 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 3 of A200871.

Programs

Mathematica

a[0,x_,y_] := 1; a[n_,x_,y_] := a[n,x,y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 4}]; a[n_] := Sum[a[n, x, y], {x, 4}, {y, 4}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)

Formula

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

Empirical g.f.: 2*x*(18 + 11*x + 6*x^2 + 18*x^3 + 8*x^4) / (1 - 2*x - x^2 - 2*x^4 - x^5). - Colin Barker, Oct 15 2017