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A224168 Number of n X 3 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224168 #11 Mar 18 2025 20:54:48
%S A224168 50,684,4739,22988,87878,282372,794220,2010035,4668304,10095924,
%T A224168 20559019,39765666,73565736,130901340,225070360,375375241,609239622,
%U A224168 964886492,1494683371,2269272536,3382617538,4958111188,7155904828,10181634047
%N A224168 Number of n X 3 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224168 R. H. Hardin, <a href="/A224168/b224168.txt">Table of n, a(n) for n = 1..210</a>
%F A224168 Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9083/30240)*n^7 + (1039/720)*n^6 + (46769/8640)*n^5 + (3863/360)*n^4 + (411149/22680)*n^3 + (14863/1260)*n^2 + (6497/1260)*n - 3.
%F A224168 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224168 G.f.: x*(50 + 184*x + 149*x^2 + 378*x^3 - 327*x^4 + 412*x^5 - 228*x^6 + 107*x^7 - 22*x^8 + 3*x^9) / (1 - x)^10.
%F A224168 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 A224168 (End)
%e A224168 Some solutions for n=3:
%e A224168 ..0..0..1....1..1..0....2..2..2....0..0..1....0..0..1....1..0..0....2..2..1
%e A224168 ..1..2..1....2..1..0....2..2..2....1..2..1....0..0..1....2..3..2....3..3..1
%e A224168 ..2..2..3....2..3..3....2..2..3....3..3..1....0..2..2....3..3..3....3..3..3
%Y A224168 Column 3 of A224173.
%K A224168 nonn
%O A224168 1,1
%A A224168 _R. H. Hardin_, Mar 31 2013
%E A224168 Name corrected by _Andrew Howroyd_, Mar 18 2025