OFFSET
0,3
COMMENTS
Number of bisymmetric, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n} that have annihilator elements.
Apart from the offset the same as A131128. - R. J. Mathar, Jan 02 2018
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
J. Devillet, Bisymmetric and quasitrivial operations: characterizations and enumerations, arXiv:1712.07856 [math.RA] (2017).
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = A296953(n)-2, a(0)=0, a(1)=1.
From Colin Barker, Dec 22 2017: (Start)
G.f.: x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)).
a(n) = 3*2^(n-1) - 4 for n>1.
a(n) = 3*a(n-1) - 2*a(n-2) for n>3.
(End)
MATHEMATICA
CoefficientList[Series[x (1 - x + 4 x^2)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* Michael De Vlieger, Dec 23 2017 *)
LinearRecurrence[{3, -2}, {0, 1, 2, 8}, 40] (* Harvey P. Dale, Jun 05 2021 *)
PROG
(PARI) concat(0, Vec(x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ Colin Barker, Dec 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
J. Devillet, Dec 22 2017
EXTENSIONS
G.f. in the name replaced by a better g.f. by Colin Barker, Dec 23 2017
STATUS
approved