A267229 Number of length-n 0..5 arrays with no following elements greater than or equal to the first repeated value.

6, 36, 195, 1030, 5375, 27854, 143695, 738990, 3791775, 19421854, 99344735, 507597950, 2591191375, 13217410254, 67376465775, 343259079310, 1747901098175, 8896431461054, 45262405898815, 230195833919070, 1170328696616175, 5948113914182254, 30221815238075855

Offset: 1

Author

R. H. Hardin, Jan 12 2016

Keywords

• nonn

Comments

Column 5 of A267232.

Examples

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

Links

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

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 20*a(n-1) -160*a(n-2) +650*a(n-3) -1399*a(n-4) +1490*a(n-5) -600*a(n-6) for n>7.

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

G.f.: x*(6 - 84*x + 435*x^2 - 1010*x^3 + 969*x^4 - 172*x^5 - 120*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)^2).

a(n) = (-5*(15 + 5*2^(1+n) + 10*3^n + 15*4^n - 97*5^n) + 12*5^n*n) / 300 for n>1. (End)