A020519 11th cyclotomic polynomial evaluated at powers of 2.

11, 2047, 1398101, 1227133513, 1172812402961, 1162219258676257, 1171221845949812801, 1189887617730934227073, 1213666705181745367548161, 1240362622532514091484054017, 1268889750375080065623288448001, 1298708349570020393652962442872833

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..332

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

Formula

G.f.: -(72022409665839104*x^10 -95936100375199744*x^9 +41035167933923328*x^8 -7266644321632256*x^7 +581441424424960*x^6 -21804053415936*x^5 +388080675136*x^4 -3261182144*x^3 +12564486*x^2 -20470*x +11) / ((x -1)*(2*x -1)*(4*x -1)*(8*x -1)*(16*x -1)*(32*x -1)*(64*x -1)*(128*x -1)*(256*x -1)*(512*x -1)*(1024*x -1)). - Colin Barker, Feb 14 2015

a(n) = 1+2^n+4^n+8^n+16^n+32^n+64^n+128^n+256^n+512^n+1024^n. - Colin Barker, Feb 15 2015

a(n) = A060885(A000079(n)). - Michel Marcus, Apr 06 2016

Maple

with(numtheory, cyclotomic):seq(cyclotomic(11, 2^i), i=0..24);

Mathematica

Table[Total[x^Range[0, 10]], {x, 2^Range[0, 10]}] (* Harvey P. Dale, Mar 05 2014 *)

Prog

(PARI) a(n) = polcyclo(11, 2^n); \\ Michel Marcus, Apr 12 2014

Crossrefs

Cf. A000079, A060885.

Sequence in context: A167249 A180587 A060885 * A004822 A265876 A078271

Adjacent sequences: A020516 A020517 A020518 * A020520 A020521 A020522

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved