A060896 a(n) = n^12 - n^6 + 1.

1, 1, 4033, 530713, 16773121, 244125001, 2176735681, 13841169553, 68719214593, 282429005041, 999999000001, 3138426605161, 8916097462273, 23298080295673, 56693904845761, 129746326500001, 281474959933441, 582622213092193, 1156831347413953, 2213314872020281, 4095999936000001

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

Comments

a(n) = Phi_36(n) where Phi_k 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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Programs

Maple

A060896 := proc(n)
        numtheory[cyclotomic](36,n) ;
end proc:
seq(A060896(n),n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Table[n^12-n^6+1,{n,0,30}] (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{1,1,4033,530713,16773121,244125001,2176735681,13841169553,68719214593,282429005041,999999000001,3138426605161,8916097462273},30] (* Harvey P. Dale, Dec 16 2013 *)

PARI

a(n) = { n^12 - n^6 + 1 } \\ Harry J. Smith, Jul 19 2009

Formula

G.f.: -(x^12 +4020*x^11 +478362*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 +478076*x^3 +4098*x^2 -12*x +1)/(x -1)^13. - Colin Barker, Oct 29 2012

a(0)=1, a(1)=1, a(2)=4033, a(3)=530713, a(4)=16773121, a(5)=244125001, a(6)=2176735681, a(7)=13841169553, a(8)=68719214593, a(9)=282429005041, a(10)=999999000001, a(11)=3138426605161, a(12)=8916097462273, a(n)=13*a(n-1)- 78*a(n-2)+ 286*a(n-3)- 715*a(n-4)+ 1287*a(n-5)- 1716*a(n-6)+ 1716*a(n-7)- 1287*a(n-8)+ 715*a(n-9)- 286*a(n-10)+ 78*a(n-11)- 13*a(n-12)+ a(n-13). - Harvey P. Dale, Dec 16 2013