%I
%S 7,304,9958,288280,7973053,217032088,5875893676,158794026640,
%T 4288744989139,115807878426592,3126918614998354,84427755760664680,
%U 2279557984193621065,61548142781949118216,1661800549993751359192,44868621103769828836000,1211452826087259054393631
%N The number of combinatorial equivalence classes of nendomorphisms on a rank3 semigroup.
%C An nendomorphism of a free semigroup is an endomorphism that sends every generator to a word of length <= n. Two nendomorphisms are combinatorially equivalent if they are conjugate under an automorphism of the semigroup. This sequence gives the number of combinatorial equivalence classes of nendomorphisms on a rank3 semigroup, for n=1,2,3,...
%H Louis Rubin and Brian Rushton, <a href="http://arxiv.org/abs/1412.3001">Combinatorial Equivalence of mEndomorphisms</a>, arXiv:1412.3001 [math.CO], 20142015.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (44,553,2760,6219,6156,2187).
%F a(n) = (1/6)*(((3^(n+1)3)/2)^3+3*n*((3^(n+1)3)/2)+2*((3^(n+1)3)/2)) = (3^n1)*(12*n + 17 + 9*(9^n  2*3^n))/16. [simplified by_Giovanni Resta_]
%F G.f.: x*(7  4*x + 453*x^2  1080*x^3)/((1  36*x + 243*x^2)*(1  4*x + 3*x^2)^2). [_Bruno Berselli_, May 19 2015]
%t Table[(3^n1)(12 n + 17 + 9 (9^n  2 3^n))/16, {n, 20}] (* _Giovanni Resta_, May 19 2015 *)
%o (MAGMA) [(3^n1)*(12*n+17+9*(9^n2*3^n))/16: n in [1..20]]; // _Bruno Berselli_, May 19 2015
%Y Cf. A134057, which gives the number of classes for a rank2 semigroup.
%Y Cf. A006516, which gives the number of classes for a rank2 monoid.
%K nonn,easy
%O 1,1
%A _Louis J. Rubin_, May 18 2015
