A083074 a(n) = n^3 - n^2 - n - 1.

-1, -2, 1, 14, 43, 94, 173, 286, 439, 638, 889, 1198, 1571, 2014, 2533, 3134, 3823, 4606, 5489, 6478, 7579, 8798, 10141, 11614, 13223, 14974, 16873, 18926, 21139, 23518, 26069, 28798, 31711, 34814, 38113, 41614, 45323, 49246, 53389, 57758, 62359, 67198, 72281

Offset: 0

Author

Paul Barry, Apr 21 2003

Keywords

• easy
• sign

Comments

Values of tribonacci polynomial n^3 - n^2 - n - 1 for n >= 0. - Artur Jasinski, Nov 19 2006

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..780
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Apart from initial terms, a column of A083064.

Cf. A000027, A002378, A028387.

Programs

Magma

[n^3 - n^2 - n - 1: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011

Mathematica

Table[n^3 - n^2 - n - 1, {n, 0, 41}] (* Artur Jasinski, Nov 19 2006 *)
LinearRecurrence[{4,-6,4,-1},{-1,-2,1,14},50] (* Harvey P. Dale, Oct 11 2020 *)

PARI

a(n)=n^3-n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = n^3 + 5*n^2 + 7*n + 1 = (n*(n + 2)^3 + 1)/(n + 1) [with a different offset].

G.f.: (2*x^3+3*x^2+2*x-1)/(x-1)^4. - Alois P. Heinz, Jan 25 2023

From Elmo R. Oliveira, Aug 08 2025: (Start)

E.g.f.: exp(x)*(-1 - x + 2*x^2 + x^3).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Extensions

Simpler definition from Alonso del Arte, Sep 16 2004