A200872 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.

10, 37, 94, 195, 356, 595, 932, 1389, 1990, 2761, 3730, 4927, 6384, 8135, 10216, 12665, 15522, 18829, 22630, 26971, 31900, 37467, 43724, 50725, 58526, 67185, 76762, 87319, 98920, 111631, 125520, 140657, 157114, 174965, 194286, 215155, 237652, 261859

Offset: 1

Author

R. H. Hardin, Nov 23 2011

Keywords

• nonn

Comments

Row 2 of A200871.

Examples

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

Links

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

Formula

Empirical: a(n) = (1/12)*n^4 + (3/2)*n^3 + (47/12)*n^2 + (7/2)*n + 1.

Conjectures from Colin Barker, Oct 16 2017: (Start)

G.f.: x*(10 - 13*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)