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

0,2

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).

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

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A000040, A000215, A019434.

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

Sequence in context: A094904 A286456 A352209 * A126439 A318541 A076903

Adjacent sequences: A171660 A171661 A171662 * A171664 A171665 A171666

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 14 2009

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

Status

approved