A267240 Number of n X 3 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.

4, 13, 42, 141, 486, 1685, 5804, 19769, 66544, 221581, 730918, 2391717, 7772610, 25110933, 80713016, 258280817, 823269116, 2615088973, 8281113730, 26150883901, 82375282494, 258893742933, 811984918692, 2541865829801, 7943330715176

Offset

1,1

Links

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

Robert Israel, Maple-assisted proof of empirical recurrence

Formula

Empirical: a(n) = 10*a(n-1) - 39*a(n-2) + 76*a(n-3) - 79*a(n-4) + 42*a(n-5) - 9*a(n-6).

Conjectures from Colin Barker, Jan 11 2019: (Start)

G.f.: x*(4 - 27*x + 68*x^2 - 76*x^3 + 42*x^4 - 9*x^5) / ((1 - x)^4*(1 - 3*x)^2).

a(n) = (24 + (31+3^(2+n))*n + 12*n^2 + 2*n^3) / 24.

(End)

Empirical recurrence verified (see link). - Robert Israel, Sep 08 2019

Example

Some solutions for n=4:
..0..0..1....0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..0..1
..0..1..0....0..1..0....0..1..1....0..0..1....0..1..0....0..0..1....1..1..0
..1..0..0....1..1..0....1..0..1....0..1..1....0..0..1....0..0..1....0..1..1
..1..1..0....1..1..1....0..1..1....0..1..1....0..0..1....1..1..0....1..0..1

Crossrefs

Column 3 of A267245.

Sequence in context: A175005 A070031 A082989 * A192802 A149425 A047144

Adjacent sequences: A267237 A267238 A267239 * A267241 A267242 A267243

Keyword

nonn

Author

R. H. Hardin, Jan 12 2016

Status

approved