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A296954 Expansion of x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)). 1
0, 1, 2, 8, 20, 44, 92, 188, 380, 764, 1532, 3068, 6140, 12284, 24572, 49148, 98300, 196604, 393212, 786428, 1572860, 3145724, 6291452, 12582908, 25165820, 50331644, 100663292, 201326588, 402653180, 805306364, 1610612732, 3221225468, 6442450940, 12884901884 (list; graph; refs; listen; history; text; internal format)
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

Cf. A296953.

Sequence in context: A096586 A165751 A131128 * A203604 A240940 A066857

Adjacent sequences:  A296951 A296952 A296953 * A296955 A296956 A296957

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

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Last modified August 14 06:54 EDT 2022. Contains 356110 sequences. (Running on oeis4.)