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

1,1

Comments

Column 7 of A267471.

Links

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

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)

Example

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

Crossrefs

Cf. A267471.

Sequence in context: A146885 A122093 A267231 * A227591 A268943 A269639

Adjacent sequences: A267467 A267468 A267469 * A267471 A267472 A267473

Keyword

nonn

Author

R. H. Hardin, Jan 15 2016

Status

approved