A267466 Number of length-n 0..3 arrays with no following elements larger than the first repeated value.

4, 16, 58, 204, 712, 2490, 8770, 31200, 112300, 409254, 1510102, 5638956, 21290368, 81183858, 312262954, 1210023672, 4718194516, 18492663102, 72787129726, 287468548548, 1138446338344, 4518338475786, 17963524388818, 71514144464784

Offset

1,1

Comments

Column 3 of A267471.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) -65*a(n-2) +155*a(n-3) -174*a(n-4) +72*a(n-5).

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

G.f.: 2*x*(2 - 18*x + 55*x^2 - 65*x^3 + 23*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2*(1 - 4*x)).

a(n) = (-18 - 9*2^(1+n) + 50*3^n + 9*4^n + 4*3^n*n) / 36.

(End)

Example

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

Crossrefs

Cf. A267471.

Sequence in context: A126644 A168583 A092688 * A255299 A123889 A180143

Adjacent sequences: A267463 A267464 A267465 * A267467 A267468 A267469

Keyword

nonn

Author

R. H. Hardin, Jan 15 2016

Status

approved