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Number of 3X3 3 X 3 0..n arrays with rows and columns in lexicographically nondecreasing order.

Row 3 of A229794

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)

Some solutions for n=2:

Row 3 of A229794.

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R. H. Hardin, <a href="/A229796/b229796.txt">Table of n, a(n) for n = 1..207</a>

allocated for R. H. Hardin

Number of 3X3 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

1,1

Row 3 of A229794

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

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

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nonn

R. H. Hardin, Sep 29 2013

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