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

Author

R. H. Hardin, Jan 12 2016

Keywords

• nonn

Comments

Column 7 of A267232.

Examples

			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
		

Links

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

Crossrefs

Cf. A267232.

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)