A171663 - OEIS

%I #26 Nov 05 2025 15:22:18

%S 1,5,5,13,25,41,113,145,481,545,1985,2113,8065,8321,32513,33025,

%T 130561,131585,523265,525313,2095105,2099201,8384513,8392705,33546241,

%U 33562625,134201345,134234113,536838145,536903681,2147418113,2147549185

%N 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 G. C. Greubel, <a href="/A171663/b171663.txt">Table of n, a(n) for n = 0..1000</a>

%H Yu Tsumura, <a href="https://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 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-8,8).

%F 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 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 (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 (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 (SageMath) ((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 Cf. A000040, A000215, A019434.

%Y Cf. A092440, A085601 (bisections). - _R. J. Mathar_, Jan 25 2010

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Dec 14 2009

%E More terms from _R. J. Mathar_ and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010

%E New name from _Joerg Arndt_, Jun 03 2019