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

%I A229796 #7 Sep 21 2018 08:54:44
%S A229796 45,1169,14178,102251,520017,2066505,6842284,19692165,50724037,
%T A229796 119421753,261015470,535936479,1043365337,1940082033,3466044984,
%U A229796 5978361865,9995569629,16254413569,25781605914,39983353235,60755768865,90619631609
%N A229796 Number of 3 X 3 0..n arrays with rows and columns in lexicographically nondecreasing order.
%H A229796 R. H. Hardin, <a href="/A229796/b229796.txt">Table of n, a(n) for n = 1..207</a>
%F A229796 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.
%F A229796 Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F A229796 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.
%F A229796 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.
%F A229796 (End)
%e A229796 Some solutions for n=2:
%e A229796 ..0..1..1....0..0..2....0..0..0....1..1..2....1..1..1....0..2..2....0..2..2
%e A229796 ..0..1..2....1..2..1....0..2..2....1..2..0....1..1..2....1..0..2....1..0..1
%e A229796 ..2..1..0....2..0..1....0..2..2....2..0..1....2..2..1....1..2..2....1..2..1
%Y A229796 Row 3 of A229794.
%K A229796 nonn
%O A229796 1,1
%A A229796 _R. H. Hardin_, Sep 29 2013