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A293007 Expansion of 2*x^2 / (1-2*x-2*x^2). 4
0, 0, 2, 4, 12, 32, 88, 240, 656, 1792, 4896, 13376, 36544, 99840, 272768, 745216, 2035968, 5562368, 15196672, 41518080, 113429504, 309895168, 846649344, 2313089024, 6319476736, 17265131520, 47169216512, 128868696064, 352075825152, 961889042432 (list; graph; refs; listen; history; text; internal format)
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

Cf. A002605, A293005, A293006.

Essentially the same as A028860 and A152035.

Sequence in context: A109388 A302919 A181329 * A028860 A152035 A026151

Adjacent sequences:  A293004 A293005 A293006 * A293008 A293009 A293010

KEYWORD

nonn,easy

AUTHOR

J. Devillet, Sep 28 2017

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)