OFFSET
0,3
COMMENTS
Number of associative, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n} that have neutral and annihilator elements.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
M. Couceiro, J. Devillet, and J.-L. Marichal, Quasitrivial semigroups: characterizations and enumerations, arXiv:1709.09162 [math.RA] (2017).
Index entries for linear recurrences with constant coefficients, signature (2,2).
FORMULA
a(n) = 2*A002605(n-1), a(0) = 0.
a(n) = A028860(n+1), a(0) = 0.
From Colin Barker, Sep 28 2017: (Start)
a(n) = ((1-sqrt(3))^n*(1+sqrt(3)) + (-1+sqrt(3))*(1+sqrt(3))^n) / (2*sqrt(3)) for n>0.
a(n) = 2*a(n-1) + 2*a(n-2) for n>2.
(End)
PROG
(PARI) concat(vector(2), Vec(2*x^2 / (1-2*x-2*x^2) + O(x^50))) \\ Colin Barker, Sep 28 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. Devillet, Sep 28 2017
STATUS
approved