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%I #15 Apr 21 2023 02:05:34
%S 1,3,6,12,24,48,98,201,411,840,1716,3504,7156,14616,29853,60975,
%T 124542,254376,519560,1061196,2167482,4427061,9042231,18468672,
%U 37722088,77047008,157367784,321422208,656501817,1340898747,2738772998
%N An Alexander sequence for the knot 8_2.
%C The g.f. is a transformation of the g.f. 1/(1-3*x+3*x^3) of A090400 under the mapping G(x) -> (1/(1+x^2)^3)*G(x/(1+x^2)). The denominator of the g.f. is a parameterization of the Alexander polynomial for the knot 8_2.
%H G. C. Greubel, <a href="/A099844/b099844.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-3,3,-1).
%F G.f.: 1/(1 - 3*x + 3*x^2 - 3*x^3 + 3*x^4 - 3*x^5 + x^6).
%t LinearRecurrence[{3,-3,3,-3,3,-1},{1,3,6,12,24,48},40] (* _Harvey P. Dale_, Sep 18 2019 *)
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-3*x+3*x^2-3*x^3+3*x^4-3*x^5+x^6) )); // _G. C. Greubel_, Apr 20 2023
%o (SageMath)
%o def A077952_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/(1-3*x+3*x^2-3*x^3+3*x^4-3*x^5+x^6) ).list()
%o A077952_list(40) # _G. C. Greubel_, Apr 20 2023
%Y Cf. A090400, A099845.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 27 2004
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