A060892 a(n) = n^8 - n^6 + n^4 - n^2 + 1.

1, 1, 205, 5905, 61681, 375601, 1634221, 5649505, 16519105, 42521761, 99009901, 212601841, 427016305, 810932305, 1468297741, 2551550401, 4278255361, 6951703105, 10986053005, 16936647121, 25536159601, 37737287281, 54762727405, 78163228705, 109884542401

Offset

0,3

Comments

a(n) = Phi_20(n) where Phi_k(x) is the k-th cyclotomic polynomial.

Links

Harry J. Smith, Table of n, a(n) for n=0..1000

Index to values of cyclotomic polynomials of integer argument

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (1-8*x+232*x^2+4012*x^3+15958*x^4+15832*x^5+4096*x^6+196*x^7+x^8)/ (1-x)^9. [Colin Barker, Apr 22 2012]

Maple

A060892 := proc(n)
        numtheory[cyclotomic](20, n) ;
end proc:
seq(A060892(n), n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Cyclotomic[20, Range[0, 30]] (* Paolo Xausa, Feb 26 2024 *)

Prog

(PARI) a(n) = n^8 - n^6 + n^4 - n^2 + 1; \\ Harry J. Smith, Jul 14 2009

Crossrefs

Sequence in context: A203889 A226564 A077457 * A359498 A203862 A289333

Adjacent sequences: A060889 A060890 A060891 * A060893 A060894 A060895

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2001

Status

approved