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

1,1

Comments

Row 5 of A200785.

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)

Example

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

Crossrefs

Sequence in context: A306746 A332545 A269081 * A250356 A269587 A232053

Adjacent sequences: A200786 A200787 A200788 * A200790 A200791 A200792

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved