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

0,2

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).

Formula

a(n) = n^3 + 5n^2 + 7n + 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

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 *)

Prog

(Magma) [n^3 - n^2 - n - 1: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
(PARI) a(n)=n^3-n^2-n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Apart from initial terms, a column of A083064.

Cf. A000027, A028387, A002378.

Sequence in context: A124026 A106204 A290603 * A346378 A181869 A141510

Adjacent sequences: A083071 A083072 A083073 * A083075 A083076 A083077

Keyword

easy,sign

Author

Paul Barry, Apr 21 2003

Extensions

Simpler definition from Alonso del Arte, Sep 16 2004

Status

approved