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%I #27 Jun 05 2021 11:17:07
%S 0,1,2,8,20,44,92,188,380,764,1532,3068,6140,12284,24572,49148,98300,
%T 196604,393212,786428,1572860,3145724,6291452,12582908,25165820,
%U 50331644,100663292,201326588,402653180,805306364,1610612732,3221225468,6442450940,12884901884
%N Expansion of x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)).
%C Number of bisymmetric, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n} that have annihilator elements.
%C Apart from the offset the same as A131128. - _R. J. Mathar_, Jan 02 2018
%H Colin Barker, <a href="/A296954/b296954.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Devillet, <a href="https://arxiv.org/abs/1712.07856">Bisymmetric and quasitrivial operations: characterizations and enumerations</a>, arXiv:1712.07856 [math.RA] (2017).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = A296953(n)-2, a(0)=0, a(1)=1.
%F From _Colin Barker_, Dec 22 2017: (Start)
%F G.f.: x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)).
%F a(n) = 3*2^(n-1) - 4 for n>1.
%F a(n) = 3*a(n-1) - 2*a(n-2) for n>3.
%F (End)
%t CoefficientList[Series[x (1 - x + 4 x^2)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* _Michael De Vlieger_, Dec 23 2017 *)
%t LinearRecurrence[{3,-2},{0,1,2,8},40] (* _Harvey P. Dale_, Jun 05 2021 *)
%o (PARI) concat(0, Vec(x*(1 - x + 4*x^2) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ _Colin Barker_, Dec 22 2017
%Y Cf. A296953.
%K nonn,easy
%O 0,3
%A _J. Devillet_, Dec 22 2017
%E G.f. in the name replaced by a better g.f. by _Colin Barker_, Dec 23 2017
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