A020518 10th cyclotomic polynomial evaluated at powers of 2.

1, 11, 205, 3641, 61681, 1016801, 16519105, 266354561, 4278255361, 68585520641, 1098438933505, 17583600302081, 281406274007041, 4503049938657281, 72053196259835905, 1152886321308467201, 18446462603027742721, 295145653396718878721, 4722348468539854946305

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..830
• 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 (31,-310,1240,-1984,1024).

Crossrefs

Cf. A000079, A060884.

Programs

Maple

with(numtheory,cyclotomic):seq(cyclotomic(10,2^i),i=0..24);

Mathematica

Cyclotomic[10, 2^Range[0, 20]] (* Paolo Xausa, Sep 16 2024 *)

PARI

a(n) = polcyclo(10, 2^n) \\ Colin Barker, Feb 14 2015

Formula

G.f.: -(704*x^4-544*x^3+174*x^2-20*x+1) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(16*x-1)). - Colin Barker, Feb 14 2015

a(n) = 1-2^n+4^n-8^n+16^n. - Colin Barker, Feb 15 2015

a(n) = A060884(A000079(n)). - Michel Marcus, Apr 06 2016

Extensions

More terms from Colin Barker, Feb 14 2015