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

Author

R. H. Hardin, Sep 29 2013

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 3 of A229794.

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)