A229796 Number of 3 X 3 0..n arrays with rows and columns in lexicographically nondecreasing order.

45, 1169, 14178, 102251, 520017, 2066505, 6842284, 19692165, 50724037, 119421753, 261015470, 535936479, 1043365337, 1940082033, 3466044984, 5978361865, 9995569629, 16254413569, 25781605914, 39983353235, 60755768865, 90619631609

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..207

Formula

Empirical: a(n) = (1/20)*n^9 + (11/24)*n^8 + (329/180)*n^7 + (1601/360)*n^6 + (545/72)*n^5 + (347/36)*n^4 + (3367/360)*n^3 + (313/45)*n^2 + (37/10)*n + 1.

Conjectures from Colin Barker, Sep 21 2018: (Start)

G.f.: x*(45 + 719*x + 4513*x^2 + 7676*x^3 + 4687*x^4 + 420*x^5 + 121*x^6 - 46*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Row 3 of A229794.

Sequence in context: A327510 A215769 A320822 * A143400 A226981 A173000

Adjacent sequences: A229793 A229794 A229795 * A229797 A229798 A229799

Keyword

nonn

Author

R. H. Hardin, Sep 29 2013

Status

approved