A020519 11th cyclotomic polynomial evaluated at powers of 2.

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

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A000079, A060885.

Programs

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 *)

PARI

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

Formula

G.f.: -(72022409665839104*x^10 -95936100375199744*x^9 +41035167933923328*x^8 -7266644321632256*x^7 [phone]*x^6 -21804053415936*x^5 [phone]*x^4 -3261182144*x^3 [phone]*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