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

Offset

1,1

Comments

Column 5 of A267232.

Links

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

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)

Example

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

Crossrefs

Cf. A267232.

Sequence in context: A159721 A106539 A215453 * A048980 A200782 A055299

Adjacent sequences: A267226 A267227 A267228 * A267230 A267231 A267232

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved