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A200791 Number of 0..n arrays x(0..8) of 9 elements without any two consecutive increases. 1
512, 14849, 163020, 1062500, 4975322, 18514405, 58154912, 160338680, 398601390, 910893148, 1941103528, 3899741885, 7449762880, 13624665670, 23987233104, 40838614531, 67488892468, 108601809395, 170627966340, 262342539690 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A200785.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..135

FORMULA

Empirical: a(n) = (99377/362880)*n^9 + (48247/13440)*n^8 + (243673/12096)*n^7 + (60529/960)*n^6 + (2076437/17280)*n^5 + (274529/1920)*n^4 + (952027/9072)*n^3 + (152461/3360)*n^2 + (26399/2520)*n + 1.

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

G.f.: x*(512 + 9729*x + 37570*x^2 + 39065*x^3 + 11862*x^4 + 551*x^5 + 124*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

EXAMPLE

Some solutions for n=3

..0....0....0....0....0....1....1....1....3....0....1....0....1....1....3....1

..0....0....0....3....3....3....3....3....0....3....3....3....0....1....1....3

..3....0....2....0....1....0....0....1....0....2....3....3....2....2....0....1

..2....1....0....3....0....3....0....3....1....2....1....3....1....2....1....0

..2....1....3....3....0....0....2....3....0....3....1....1....0....3....1....0

..3....3....2....0....3....0....0....1....2....3....3....0....3....2....3....2

..2....2....2....3....2....2....0....1....1....1....2....1....1....0....1....1

..1....3....3....2....3....0....0....3....1....0....2....1....0....1....0....0

..3....0....1....2....3....1....3....2....3....2....2....0....0....0....3....2

CROSSREFS

Sequence in context: A256947 A254720 A254252 * A254812 A329894 A258523

Adjacent sequences:  A200788 A200789 A200790 * A200792 A200793 A200794

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 22 2011

STATUS

approved

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Last modified October 15 18:54 EDT 2021. Contains 348034 sequences. (Running on oeis4.)