A200787 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases.

32, 216, 840, 2425, 5796, 12152, 23136, 40905, 68200, 108416, 165672, 244881, 351820, 493200, 676736, 911217, 1206576, 1573960, 2025800, 2575881, 3239412, 4033096, 4975200, 6085625, 7385976, 8899632, 10651816, 12669665, 14982300

Offset: 1

Author

R. H. Hardin, Nov 22 2011

Keywords

• nonn

Comments

Row 3 of A200785.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..139

Formula

Empirical: a(n) = (7/12)*n^5 + (47/12)*n^4 + (39/4)*n^3 + (133/12)*n^2 + (17/3)*n + 1.

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

G.f.: x*(32 + 24*x + 24*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = (1 + n)^2*(12 + 44*n + 33*n^2 + 7*n^3) / 12 .

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)