A214731 a(n) = n^3 - 2*n^2 - 1.

-2, -1, 8, 31, 74, 143, 244, 383, 566, 799, 1088, 1439, 1858, 2351, 2924, 3583, 4334, 5183, 6136, 7199, 8378, 9679, 11108, 12671, 14374, 16223, 18224, 20383, 22706, 25199, 27868, 30719, 33758, 36991, 40424, 44063, 47914, 51983, 56276, 60799, 65558, 70559

Offset: 1

Author

Marco Piazzalunga, Jul 27 2012

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A080859, A085490, A144390 (first differences), A152619.

Similar sequences: A152015 (of the type m^3+2m^2-1), A081437 (m^3-2m^2+1).

Programs

Magma

[n^3-2*n^2-1: n in [1..50]]; // Vincenzo Librandi, Jul 29 2012

Maple

A214731:=n->n^3-2*n^2-1: seq(A214731(n), n=1..60); # Wesley Ivan Hurt, Apr 18 2017

Mathematica

Table[n^3 - 2 n^2 - 1, {n, 50}] (* Vincenzo Librandi, Jul 29 2012 *)

PARI

a(n)=n^3-2*n^2-1 \\ Charles R Greathouse IV, Jul 27 2012

SageMath

[n^2*(n-2)-1 for n in range(1,51)] # G. C. Greubel, Dec 31 2023

Formula

From Bruno Berselli, Jul 27 2012: (Start)

G.f.: -x*(2-7*x-x^3)/(1-x)^4.

a(n) = A085490(n-1) + 2.

a(n) = A152619(n-2) - 1 for n>1.

a(n) - a(n-2) = A080859(n-2) - 1 for n>2. (End)

E.g.f.: 1 - (1-x)*(1+x)^2*exp(x). - G. C. Greubel, Dec 31 2023

Extensions

a(3) corrected by Charles R Greathouse IV, Jul 27 2012