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A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.

%I A224186 #8 Aug 29 2018 05:57:53
%S A224186 46,548,3526,15779,55438,163746,424326,992607,2138488,4305730,8191976,
%T A224186 14853709,25840868,43366252,70515252,111501861,171977322,259398184,
%U A224186 383460946,556610879,794633026,1117333790,1549321930,2120898195
%N A224186 Number of n X 4 0..2 arrays with rows unimodal and columns nondecreasing.
%C A224186 Column 4 of A224190.
%H A224186 R. H. Hardin, <a href="/A224186/b224186.txt">Table of n, a(n) for n = 1..210</a>
%F A224186 Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1.
%F A224186 Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F A224186 G.f.: x*(46 + 134*x + 250*x^2 - 91*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.
%F A224186 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A224186 (End)
%e A224186 Some solutions for n=3:
%e A224186 ..0..1..0..0....1..1..1..1....2..1..0..0....0..1..2..0....0..1..0..0
%e A224186 ..1..1..0..0....1..1..1..1....2..1..1..0....0..2..2..0....0..1..1..0
%e A224186 ..1..2..0..0....1..1..1..1....2..2..1..1....0..2..2..0....1..1..1..0
%Y A224186 Cf. A224190.
%K A224186 nonn
%O A224186 1,1
%A A224186 _R. H. Hardin_, Apr 01 2013