A200786 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases.

16, 75, 225, 530, 1071, 1946, 3270, 5175, 7810, 11341, 15951, 21840, 29225, 38340, 49436, 62781, 78660, 97375, 119245, 144606, 173811, 207230, 245250, 288275, 336726, 391041, 451675, 519100, 593805, 676296, 767096, 866745, 975800, 1094835

Offset: 1

Author

R. H. Hardin, Nov 22 2011

Keywords

• nonn

Comments

Row 2 of A200785.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..140
• A. Burstein and T. Mansour, Words restricted by 3-letter generalized multipermutation patterns, Annals. Combin., 7 (2003), 1-14. See Th. 3.13.

Formula

Empirical: a(n) = (17/24)*n^4 + (43/12)*n^3 + (151/24)*n^2 + (53/12)*n + 1.

Conjectures from Colin Barker, Oct 15 2017: (Start)

G.f.: x*(16 - 5*x + 10*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = (24 + 106*n + 151*n^2 + 86*n^3 + 17*n^4) / 24.

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)