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%I #13 Aug 13 2013 20:35:29
%S 1,176,5490,65600,455875,2239776,8647716,27962880,78920325,200002000,
%T 464447126,1003294656,2039332295,3935444800,7261533000,12884914176,
%U 22089914121,36733221360,59442494650,93866696000,144987663051,219503536736,326295822700,476993088000
%N 1/6 the number of colorings of a 3 X 3 rhombic- or staggered- hexagonal array with n colors.
%C Numbers for rhombic- and staggered- hexagonal arrays differ above 4 X 4.
%H Alois P. Heinz, <a href="/A068244/b068244.txt">Table of n, a(n) for n = 3..1000</a>
%F From _Alois P. Heinz_, May 02 2012: (Start)
%F G.f.: (1089*x^6+10934*x^5+26015*x^4+18500*x^3+3775*x^2+166*x+1) / (x-1)^10*x^3.
%F a(n) = (n^9 -16*n^8 +112*n^7 -448*n^6 +1120*n^5 -1791*n^4 +1786*n^3 -1012*n^2 +248*n)/6. (End)
%p a:= n-> (248 +(-1012 +(1786 +(-1791 +(1120 +(-448 +(112 +(-16+n)*n) *n) *n) *n) *n) *n) *n) *n/6:
%p seq(a(n), n=3..40); # _Alois P. Heinz_, May 02 2012
%Y Cf. A068239-A068305, A000332, A002417, A027441, A212162, A212163.
%K nonn
%O 3,2
%A _R. H. Hardin_, Feb 24 2002
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