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%I #10 Jul 11 2018 08:36:38
%S 192,3645,28672,140625,513216,1529437,3932160,9034497,19000000,
%T 37202781,68677632,120670225,203297472,330328125,520093696,796539777,
%U 1190427840,1740697597,2496000000,3516410961,4875335872,6661615005,8981839872
%N Number of 3 X 3 0..n arrays with every element equal to a diagonal or antidiagonal reflection.
%C Row 3 of A209593.
%H R. H. Hardin, <a href="/A209594/b209594.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = (n+1) ^ 6 * (2*n+1).
%F From _Colin Barker_, Jul 11 2018: (Start)
%F G.f.: x*(192 + 2109*x + 4888*x^2 + 2557*x^3 + 352*x^4 - 25*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
%F (End)
%e Some solutions for n=3:
%e ..2..1..2....3..3..2....0..2..0....1..2..3....1..2..1....2..2..1....0..3..1
%e ..1..3..2....3..1..1....2..2..0....2..3..1....0..2..2....2..3..0....2..1..3
%e ..3..2..0....2..1..3....0..0..3....2..1..0....2..0..2....0..0..0....2..2..3
%o (PARI) a(n) = (2*n+1)*(n+1)^6; \\ _Altug Alkan_, Jul 11 2018
%Y Cf. A209593.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 10 2012
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