A222001 Number of n X 3 arrays with each row a permutation of 1..3 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.

6, 12, 22, 37, 58, 86, 122, 167, 222, 288, 366, 457, 562, 682, 818, 971, 1142, 1332, 1542, 1773, 2026, 2302, 2602, 2927, 3278, 3656, 4062, 4497, 4962, 5458, 5986, 6547, 7142, 7772, 8438, 9141, 9882, 10662, 11482, 12343, 13246, 14192, 15182, 16217, 17298

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

Conjectures from Colin Barker, Aug 14 2018: (Start)

G.f.: x*(6 - 12*x + 10*x^2 - 3*x^3) / (1 - x)^4.

a(n) = 2 + (1 + n)*(2 + n)*(3 + n) / 6.

(End)

Example

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

Crossrefs

Column 3 of A222005.

Sequence in context: A344033 A266085 A144568 * A078472 A192754 A005694

Adjacent sequences: A221998 A221999 A222000 * A222002 A222003 A222004

Keyword

nonn

Author

R. H. Hardin, Feb 03 2013

Status

approved