A267470 Number of length-n 0..7 arrays with no following elements larger than the first repeated value.

8, 64, 484, 3592, 26440, 193852, 1418740, 10378144, 75944464, 556295860, 4080955516, 29994246136, 220942982968, 1631599880428, 12082194095812, 89736369169168, 668588308469152, 4997804102441956, 37486765952804428

Offset: 1

Author

R. H. Hardin, Jan 15 2016

Keywords

• nonn

Comments

Column 7 of A267471.

Examples

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

Links

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

Crossrefs

Cf. A267471.

Formula

Empirical: a(n) = 43*a(n-1) -798*a(n-2) +8358*a(n-3) -54201*a(n-4) +224427*a(n-5) -589112*a(n-6) +936452*a(n-7) -807408*a(n-8) +282240*a(n-9).

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

G.f.: 4*x*(2 - 70*x + 1029*x^2 - 8253*x^3 + 39228*x^4 - 112119*x^5 + 185785*x^6 - 160106*x^7 + 53244*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)^2*(1 - 8*x)).

a(n) = (-980 - 147*2^(2+n) - 245*2^(1+2*n) - 490*3^n - 245*2^(2+n)*3^n - 588*5^n + 7818*7^n + 735*8^n + 120*7^n*n) / 5880.

(End)