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A223719 Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.

%I A223719 #7 Feb 19 2018 09:27:52
%S A223719 9,81,484,2116,7396,21904,57121,134689,292681,594441,1140624,2085136,
%T A223719 3655744,6180196,10118761,16104169,24990001,37908649,56340036,
%U A223719 82192356,117896164,166513216,231861529,318658201,432681601,580954609,771950656
%N A223719 Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.
%C A223719 Column 2 of A223725.
%H A223719 R. H. Hardin, <a href="/A223719/b223719.txt">Table of n, a(n) for n = 1..210</a>
%F A223719 Empirical: a(n) = (1/576)*n^8 + (1/48)*n^7 + (41/288)*n^6 + (13/24)*n^5 + (793/576)*n^4 + (31/16)*n^3 + (119/48)*n^2 + (3/2)*n + 1.
%F A223719 Conjectures from _Colin Barker_, Feb 19 2018: (Start)
%F A223719 G.f.: x*(9 + 79*x^2 - 80*x^3 + 106*x^4 - 68*x^5 + 31*x^6 - 8*x^7 + x^8) / (1 - x)^9.
%F A223719 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 A223719 (End)
%e A223719 Some solutions for n=3:
%e A223719 ..1..0....2..0....1..2....2..0....1..1....2..0....0..2....2..1....1..1....2..2
%e A223719 ..1..2....1..2....1..2....0..0....2..2....2..1....2..0....1..1....2..1....1..2
%e A223719 ..2..1....1..0....1..2....0..1....0..1....0..0....2..0....1..2....1..1....1..1
%K A223719 nonn
%O A223719 1,1
%A A223719 _R. H. Hardin_, Mar 26 2013