A060893 a(n) = n^8 - n^4 + 1.

1, 1, 241, 6481, 65281, 390001, 1678321, 5762401, 16773121, 43040161, 99990001, 214344241, 429960961, 815702161, 1475750641, 2562840001, 4294901761, 6975673921, 11019855601, 16983432721, 25599840001, 37822664881, 54875639281, 78310705441, 110074982401

Offset

0,3

Comments

a(n) = Phi_24(n) where Phi_k(x) is the k-th cyclotomic polynomial.

Links

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

Hisanori Mishima, Factorizations of many number sequences

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+268*x^2+4264*x^3+15670*x^4+15544*x^5+4348*x^6+232*x^7+x^8)/ (1-x)^9. - Colin Barker, Apr 22 2012

a(0)=1, a(1)=1, a(2)=241, a(3)=6481, a(4)=65281, a(5)=390001, a(6)=1678321, a(7)=5762401, a(8)=16773121, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Nov 03 2014

Maple

A060893 := proc(n)
        numtheory[cyclotomic](24, n) ;
end proc:
seq(A060893(n), n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Table[n^8-n^4+1, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 1, 241, 6481, 65281, 390001, 1678321, 5762401, 16773121}, 30] (* Harvey P. Dale, Nov 03 2014 *)

Prog

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

Crossrefs

Sequence in context: A165383 A006687 A372966 * A165375 A183887 A007205

Adjacent sequences: A060890 A060891 A060892 * A060894 A060895 A060896

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2001

Status

approved