A060896 n^12 - n^6 + 1.

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

Offset

0,3

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).

Formula

G.f.: -(x^12 +4020*x^11 +478362*x^10 +10188140*x^9 +66317319*x^8 +162512496*x^7 +162514212*x^6 +66316032*x^5 +10188855*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

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 *)

Prog

(PARI) { for (n=0, 1000, write("b060896.txt", n, " ", n^12 - n^6 + 1); ) } \\ Harry J. Smith, Jul 19 2009

Crossrefs

Sequence in context: A234838 A234834 A212601 * A371757 A206617 A252686

Adjacent sequences: A060893 A060894 A060895 * A060897 A060898 A060899

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2001

Status

approved