A200784 Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases.

456, 3270, 23136, 164004, 1160616, 8216484, 58154912, 411637168, 2913595712, 20622837480, 145970677056, 1033197881712, 7313093248992, 51762926098992, 366383987227392, 2593308396911680, 18355737644921600, 129924040926296800

Offset

1,1

Comments

Column 7 of A200785.

Links

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

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

Empirical g.f.: 2*x*(228 - 189*x - 1512*x^2 + 2226*x^3 - 108*x^4 - 864*x^5 + 256*x^6) / ((1 - 2*x)*(1 + 2*x - 2*x^2)*(1 - 8*x + 6*x^2 + 4*x^3 - 2*x^4)). - Colin Barker, Oct 15 2017

Example

Some solutions for n=3
..7....5....7....4....5....2....3....7....5....5....5....6....1....5....4....4
..0....5....4....2....3....2....1....4....0....5....7....4....0....5....4....4
..0....5....4....1....6....6....3....5....0....4....6....6....6....7....4....4
..0....1....7....1....5....5....0....0....6....1....6....3....0....0....4....7
..1....4....0....6....5....2....6....5....3....4....2....4....1....2....4....3

Crossrefs

Sequence in context: A265493 A265600 A222552 * A077578 A329756 A268162

Adjacent sequences: A200781 A200782 A200783 * A200785 A200786 A200787

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved