A259348 a(n) = n^3 - 8.

-8, -7, 0, 19, 56, 117, 208, 335, 504, 721, 992, 1323, 1720, 2189, 2736, 3367, 4088, 4905, 5824, 6851, 7992, 9253, 10640, 12159, 13816, 15617, 17568, 19675, 21944, 24381, 26992, 29783, 32760, 35929, 39296, 42867, 46648, 50645, 54864, 59311, 63992

Offset: 0

Author

Luciano Ancora, Jun 24 2015

Keywords

• sign
• easy

Comments

The cubic number sequence whose geometrical arrangement loses all vertices: this is a figurate number represented by a cubic lattice of n^3 equispaced points without vertices.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[n^3 - 8: n in [0..40]]; // Vincenzo Librandi, Jun 25 2015

Mathematica

Table[n^3 - 8, {n, 0, 40}] (* Vincenzo Librandi, Jun 25 2015 *)
LinearRecurrence[{4,-6,4,-1},{-8,-7,0,19},50] (* Harvey P. Dale, Sep 25 2017 *)

Formula

G.f.: (-8 + 25*x - 20*x^2 + 9*x^3)/(1-x)^4. - Vincenzo Librandi, Jun 25 2015

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 25 2015

Extensions

First term -8 added from Vincenzo Librandi, Jun 25 2015