A060891 a(n) = n^6 - n^3 + 1.

1, 1, 57, 703, 4033, 15501, 46441, 117307, 261633, 530713, 999001, 1770231, 2984257, 4824613, 7526793, 11387251, 16773121, 24132657, 34006393, 47039023, 63992001, 85756861, 113369257, 148023723, 191089153, 244125001, 308898201

Offset

0,3

Comments

a(n) = Phi_18(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 (7, -21, 35, -35, 21, -7, 1).

Formula

G.f.: (1-6*x+71*x^2+290*x^3+309*x^4+52*x^5+3*x^6)/(1-x)^7. [Colin Barker, Apr 22 2012]

Maple

with (combinat):seq(fibonacci(3, n^3)-n^3, n=0..30); # Zerinvary Lajos, May 25 2008
# Alternative
A060891 := proc(n)
        numtheory[cyclotomic](18, n) ;
end proc:
seq(A060891(n), n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Array[#^6 - #^3 + 1 &, 51, 0] (* or *)
Cyclotomic[18, Range[0, 50]] (* Paolo Xausa, Feb 26 2024 *)

Prog

(PARI) { for (n=0, 1000, write("b060891.txt", n, " ", n^6 - n^3 + 1); ) } \\ Harry J. Smith, Jul 14 2009
(PARI) a(n) = polcyclo(18, n); \\ Michel Marcus, Dec 16 2017

Crossrefs

Sequence in context: A195606 A232875 A084220 * A241967 A098995 A210156

Adjacent sequences: A060888 A060889 A060890 * A060892 A060893 A060894

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2001

Status

approved