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A020515 a(n) = 4^n - 2^n + 1. 12
1, 3, 13, 57, 241, 993, 4033, 16257, 65281, 261633, 1047553, 4192257, 16773121, 67100673, 268419073, 1073709057, 4294901761, 17179738113, 68719214593, 274877382657, 1099510579201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

6th cyclotomic polynomial evaluated at powers of 2.

Referred to as Kasami-Welch numbers by Aubry et al. (see links). The first prime values are a(1) = 3, a(2) = 13, a(4) = 241, a(32) = 18446744069414584321, no more for n less than or equal to 100. - Jonathan Vos Post, Sep 15 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..170

Yves Aubry, Gary Mcguire, Francois Rodier, A few more functions that are not APN infinitely often, arXiv:0909.2304 [math.AG], 2009.

Quynh Nguyen, Jean Pedersen, and Hien T. Vu, New Integer Sequences Arising From 3-Period Folding Numbers, Vol. 19 (2016), Article 16.3.1.

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

FORMULA

From Mohammad K. Azarian, Jan 15 2009: (Start)

G.f.: 1/(1-4*x) - 1/(1-2*x) + 1/(1-x).

E.g.f.: e^(4*x) - e^(2*x) + e^x. (End)

a(n) = A002061(A000079(n)). - Michel Marcus, Apr 06 2016

MAPLE

with(numtheory, cyclotomic):seq(cyclotomic(6, 2**i), i=0..24);

PROG

(MAGMA) [4^n - 2^n + 1: n in [0..40]]; // Vincenzo Librandi, Apr 25 2011

(PARI) a(n)=4^n-2^n+1 \\ Charles R Greathouse IV, Jul 02 2013

CROSSREFS

Cf. A000079, A002061.

Sequence in context: A095934 A151220 A151221 * A049086 A010921 A275634

Adjacent sequences:  A020512 A020513 A020514 * A020516 A020517 A020518

KEYWORD

nonn,easy

AUTHOR

Simon Plouffe

STATUS

approved

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Last modified September 18 13:34 EDT 2020. Contains 337169 sequences. (Running on oeis4.)