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A229775 Number of 3 X 3 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

%I A229775 #8 Sep 21 2018 08:46:33
%S A229775 20,322,3232,21331,103222,397460,1287672,3647349,9281272,21642038,
%T A229775 46934680,95749927,185397226,343142248,610590224,1049496105,
%U A229775 1749325212,2836933738,4488787184,6946186555,10534026910,15683670652,22960578760
%N A229775 Number of 3 X 3 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.
%H A229775 R. H. Hardin, <a href="/A229775/b229775.txt">Table of n, a(n) for n = 1..210</a>
%F A229775 Empirical: a(n) = (1/120)*n^9 + (1/12)*n^8 + (133/360)*n^7 + (371/360)*n^6 + (19/9)*n^5 + (247/72)*n^4 + (403/90)*n^3 + (401/90)*n^2 + (91/30)*n + 1.
%F A229775 Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F A229775 G.f.: x*(20 + 122*x + 912*x^2 + 1101*x^3 + 912*x^4 - 125*x^5 + 118*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.
%F A229775 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 A229775 (End)
%e A229775 Some solutions for n=3:
%e A229775 ..1..0..0....1..1..0....1..0..0....1..1..1....1..1..0....1..0..0....2..0..0
%e A229775 ..1..2..0....1..1..0....1..2..0....2..1..0....2..1..2....1..3..3....2..0..0
%e A229775 ..3..3..0....3..3..0....3..2..2....3..2..2....2..2..1....3..2..0....3..1..1
%Y A229775 Row 3 of A229774.
%K A229775 nonn
%O A229775 1,1
%A A229775 _R. H. Hardin_, Sep 29 2013