A114654 Discriminant of the polynomial x^n + x + 1.

1, -3, -31, 229, 3381, -43531, -870199, 15953673, 404197705, -9612579511, -295311670611, 8630788777645, 311791207040509, -10809131718965763, -449005897206417391, 18008850183328692241, 845687005960046315793, -38519167813410200811247, -2017766063735610126699403

Offset

1,2

Comments

Except for the sign, the sequence alternates between the sum and difference of consecutive terms of A000312. x^2+x+1 divides x^n+x+1 for n=2 (mod 3).

References

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

Links

Robert Israel, Table of n, a(n) for n = 1..385

Formula

For n>1, a(n) = (n^n + (-1)^(n-1) * (n-1)^(n-1)) * (-1)^floor(n/2).

Maple

f:= n -> (n^n + (-1)^(n-1) * (n-1)^(n-1)) * (-1)^floor(n/2): f(1):= 1:
map(f, [$1..50]); # Robert Israel, Jul 01 2026

Mathematica

Table[Discriminant[x^n + x + 1, x], {n, 0, 100}] (* Artur Jasinski, Oct 12 2007 *)

Prog

(PARI) a(n) = poldisc(x^n+x+1); \\ Michel Marcus, Aug 28 2020

Crossrefs

Cf. A000312 (n^n), A007781 (n^n - (n-1)^(n-1)), A056788 (n^n + (n-1)^(n-1)), A086797 (discriminant of the polynomial x^n-x-1).

Sequence in context: A197746 A342260 A121147 * A198151 A197231 A334980

Adjacent sequences: A114651 A114652 A114653 * A114655 A114656 A114657

Keyword

sign,easy,changed

Author

T. D. Noe, Dec 21 2005

Status

approved