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A267240 Number of n X 3 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 16 11:09 EDT 2020. Contains 335784 sequences. (Running on oeis4.)