

A257919


The number of combinatorial equivalence classes of nendomorphisms on a rank3 semigroup.


0



7, 304, 9958, 288280, 7973053, 217032088, 5875893676, 158794026640, 4288744989139, 115807878426592, 3126918614998354, 84427755760664680, 2279557984193621065, 61548142781949118216, 1661800549993751359192, 44868621103769828836000, 1211452826087259054393631
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OFFSET

1,1


COMMENTS

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,...


LINKS

Table of n, a(n) for n=1..17.
Louis Rubin and Brian Rushton, Combinatorial Equivalence of mEndomorphisms, arXiv:1412.3001 [math.CO], 20142015.
Index entries for linear recurrences with constant coefficients, signature (44,553,2760,6219,6156,2187).


FORMULA

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_]
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]


MATHEMATICA

Table[(3^n1)(12 n + 17 + 9 (9^n  2 3^n))/16, {n, 20}] (* Giovanni Resta, May 19 2015 *)


PROG

(MAGMA) [(3^n1)*(12*n+17+9*(9^n2*3^n))/16: n in [1..20]]; // Bruno Berselli, May 19 2015


CROSSREFS

Cf. A134057, which gives the number of classes for a rank2 semigroup.
Cf. A006516, which gives the number of classes for a rank2 monoid.
Sequence in context: A281435 A015005 A209806 * A002437 A300870 A239163
Adjacent sequences: A257916 A257917 A257918 * A257920 A257921 A257922


KEYWORD

nonn,easy


AUTHOR

Louis J. Rubin, May 18 2015


STATUS

approved



