A267231 Number of length-n 0..7 arrays with no following elements greater than or equal to the first repeated value.

8, 64, 476, 3472, 25088, 180292, 1291052, 9222184, 65755592, 468196540, 3330042548, 23664113536, 168042120176, 1192574364148, 8459259667964, 59977781663128, 425093823838040, 3011867733313516, 21333411555220100

Offset

1,1

Comments

Column 7 of A267232.

Links

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

Formula

Empirical: a(n) = 35*a(n-1) -518*a(n-2) +4214*a(n-3) -20489*a(n-4) +60515*a(n-5) -104992*a(n-6) +96516*a(n-7) -35280*a(n-8) for n>9.

Conjectures from Colin Barker, Feb 05 2018: (Start)

G.f.: 4*x*(2 - 54*x + 595*x^2 - 3437*x^3 + 11088*x^4 - 19495*x^5 + 16287*x^6 - 3546*x^7 - 1260*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)^2).

a(n) = (-7*(70 + 21*2^(1+n) + 35*3^n + 35*2^(1+n)*3^n + 35*4^n + 42*5^n - 627*7^n) + 60*7^n*n)/2940 for n>1.

(End)

Example

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

Crossrefs

Cf. A267232.

Sequence in context: A223564 A146885 A122093 * A267470 A227591 A268943

Adjacent sequences: A267228 A267229 A267230 * A267232 A267233 A267234

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved