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A171663 Expansion of (1 + 4*x - 6*x^2 - 16*x^3 + 20*x^4)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)).

%I A171663 #24 Sep 08 2022 08:45:50
%S A171663 1,5,5,13,25,41,113,145,481,545,1985,2113,8065,8321,32513,33025,
%T A171663 130561,131585,523265,525313,2095105,2099201,8384513,8392705,33546241,
%U A171663 33562625,134201345,134234113,536838145,536903681,2147418113,2147549185
%N A171663 Expansion of (1 + 4*x - 6*x^2 - 16*x^3 + 20*x^4)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)).
%H A171663 G. C. Greubel, <a href="/A171663/b171663.txt">Table of n, a(n) for n = 0..1000</a>
%H A171663 Yu Tsumura, <a href="http://arxiv.org/abs/0912.2116">Primality tests for Fermat numbers and 2^(2k+1) +/- 2^(k+1)+1</a>, arXiv:0912.2116 [math.NT], Dec 10 2009.
%H A171663 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-8,8).
%F A171663 G.f.: (1 + 4*x - 6*x^2 - 16*x^3 + 20*x^4)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)). - _Colin Barker_, Apr 27 2013
%t A171663 Flatten[Table[2^(2*n+1) + 1 + 2^(n+1) {-1, 1}, {n, 0, 40}]] (* J. Mulder (jasper.mulder(AT)planet.nl), Jan 28 2010 *)
%o A171663 (PARI) my(x='x+O('x^40)); Vec((1+4*x-6*x^2-16*x^3+20*x^4)/((1-x)*(1- 2*x^2)*(1-4*x^2))) \\ _G. C. Greubel_, Jun 01 2019
%o A171663 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+4*x-6*x^2-16*x^3+20*x^4)/((1-x)*(1- 2*x^2)*(1-4*x^2)) )); // _G. C. Greubel_, Jun 01 2019
%o A171663 (Sage) ((1+4*x-6*x^2-16*x^3+20*x^4)/((1-x)*(1- 2*x^2)*(1-4*x^2))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 01 2019
%Y A171663 Cf. A000040, A000215, A019434.
%Y A171663 Cf. A092440, A085601 (bisections). - _R. J. Mathar_, Jan 25 2010
%K A171663 easy,nonn
%O A171663 0,2
%A A171663 _Jonathan Vos Post_, Dec 14 2009
%E A171663 More terms from _R. J. Mathar_ and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010
%E A171663 New name from _Joerg Arndt_, Jun 03 2019