%I
%S 0,1,4,9,12,25,60,121,220,441,924,1849,3612,7225,14620,29241,58140,
%T 116281,233244,466489,931612,1863225,3729180,7458361,14911260,
%U 29822521,59655964,119311929,238602012,477204025,954451740,1908903481,3817719580
%N Number of n X 3 arrays with every diagonal and antidiagonal of length L containing a permutation of 1..L.
%H R. H. Hardin, <a href="/A179808/b179808.txt">Table of n, a(n) for n=3..99</a>
%F Empirical: a(n) = 2*a(n1)a(n2)+2*a(n3)+2*a(n4)4*a(n5); G.f.: (x2*x^22*x^3+4*x^4)*x^3 / (12*x+x^22*x^32*x^4+4*x^5).
%e All solutions for 5 X 3:
%e .1.1.1...1.1.1...1.2.1...1.2.1
%e .2.2.2...2.3.2...1.3.1...1.2.1
%e .3.3.3...2.3.2...2.3.2...3.3.3
%e .1.2.1...1.3.1...2.3.2...2.2.2
%e .1.2.1...1.2.1...1.1.1...1.1.1
%K nonn
%O 3,3
%A _R. H. Hardin_, formula from _Alois P. Heinz_ in the Sequence Fans Mailing List, Jul 28 2010
