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A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223859 #8 Aug 24 2018 03:59:25
%S A223859 50,684,4884,24199,93731,303560,857696,2175884,5058530,10940664,
%T A223859 22267210,43028893,79505879,141274716,242543322,403888650,654482250,
%U A223859 1034900244,1600626232,2426368355,3611325155,5285548992,7617570604,10823463928
%N A223859 Number of n X 3 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223859 Column 3 of A223864.
%H A223859 R. H. Hardin, <a href="/A223859/b223859.txt">Table of n, a(n) for n = 1..210</a>
%F A223859 Empirical: a(n) = (353/181440)*n^9 + (353/10080)*n^8 + (9707/30240)*n^7 + (13/8)*n^6 + (45713/8640)*n^5 + (1809/160)*n^4 + (332021/22680)*n^3 + (6569/504)*n^2 + (7241/1260)*n - 2.
%F A223859 Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F A223859 G.f.: x*(50 + 184*x + 294*x^2 + 139*x^3 - 59*x^4 + 165*x^5 - 117*x^6 + 66*x^7 - 18*x^8 + 2*x^9) / (1 - x)^10.
%F A223859 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 A223859 (End)
%e A223859 Some solutions for n=3:
%e A223859 ..2..1..1....0..3..0....2..2..0....1..1..1....0..1..0....0..0..1....2..1..0
%e A223859 ..3..2..1....3..3..2....2..3..1....3..2..2....0..2..1....0..0..2....3..3..3
%e A223859 ..3..3..1....3..3..2....2..3..1....3..3..3....1..3..1....0..1..3....3..3..3
%Y A223859 Cf. A223864.
%K A223859 nonn
%O A223859 1,1
%A A223859 _R. H. Hardin_, Mar 28 2013