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A060893 n^8 - n^4 + 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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) { for (n=0, 1000, write("b060893.txt", n, " ", n^8 - n^4 + 1); ) } \\ Harry J. Smith, Jul 14 2009

CROSSREFS

Sequence in context: A220056 A165383 A006687 * A165375 A183887 A007205

Adjacent sequences:  A060890 A060891 A060892 * A060894 A060895 A060896

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 05 2001

STATUS

approved

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Last modified January 24 10:42 EST 2020. Contains 331193 sequences. (Running on oeis4.)