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)).

1, 5, 5, 13, 25, 41, 113, 145, 481, 545, 1985, 2113, 8065, 8321, 32513, 33025, 130561, 131585, 523265, 525313, 2095105, 2099201, 8384513, 8392705, 33546241, 33562625, 134201345, 134234113, 536838145, 536903681, 2147418113, 2147549185

Offset: 0

Author

Jonathan Vos Post, Dec 14 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Yu Tsumura, Primality tests for Fermat numbers and 2^(2k+1) +/- 2^(k+1)+1, arXiv:0912.2116 [math.NT], Dec 10 2009.
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-8,8).

Crossrefs

Cf. A000040, A000215, A019434.

Cf. A092440, A085601 (bisections). - R. J. Mathar, Jan 25 2010

Programs

Magma

R:=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

Mathematica

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 *)

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

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

Formula

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

Extensions

More terms from R. J. Mathar and J. Mulder (jasper.mulder(AT)planet.nl), Jan 25 2010

New name from Joerg Arndt, Jun 03 2019