A200789 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases.

128, 1791, 11704, 50775, 169884, 474566, 1160616, 2562633, 5217520, 9944957, 17946864, 30927871, 51238812, 82045260, 127523120, 193083297, 285627456, 413836891, 588496520, 822856023, 1133030140, 1538440146, 2062298520

Offset: 1

Author

R. H. Hardin, Nov 22 2011

Keywords

• nonn

Comments

Row 5 of A200785.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..137

Formula

Empirical: a(n) = (2017/5040)*n^7 + (1427/360)*n^6 + (5759/360)*n^5 + (607/18)*n^4 + (28459/720)*n^3 + (9113/360)*n^2 + (848/105)*n + 1.

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

The formulas below are consistent with the conjectured formula above.

G.f.: x*(128 + 767*x + 960*x^2 + 123*x^3 + 60*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = (5040 + 40704*n + 127582*n^2 + 199213*n^3 + 169960*n^4 + 80626*n^5 + 19978*n^6 + 2017*n^7) / 5040.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)