A152016 a(n) = n^4 - n^3 - n^2 - n.

0, -2, 2, 42, 172, 470, 1038, 2002, 3512, 5742, 8890, 13178, 18852, 26182, 35462, 47010, 61168, 78302, 98802, 123082, 151580, 184758, 223102, 267122, 317352, 374350, 438698, 511002, 591892, 682022, 782070, 892738, 1014752, 1148862

Offset

0,2

Comments

From Peter M. Chema, Jan 19 2017: (Start)

Other representations include: n (n (n (n - 1) - 1) - 1).

Real roots are 0 and 1/3 (1 + (19 - 3 sqrt(33))^(1/3) + (19 + 3 sqrt(33))^(1/3)).

Conjecture: After the 9th term, digital root is period 9: repeat [9,7,2,6,1,2,3,4,2]. (End)

From Chai Wah Wu, Mar 16 2017: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

G.f.: 2*x*(-x^3 - 6*x^2 - 6*x + 1)/(x - 1)^5. (End)

Links

Table of n, a(n) for n=0..33.

Maple

A152016:=n->n^4-n^3-n^2-n: seq(A152016(n), n=0..50); # Wesley Ivan Hurt, Jan 28 2017

Mathematica

lst={}; Do[AppendTo[lst, n^4-n^3-n^2-n], {n, 0, 5!}]; lst
(* Second program: *)
Table[Total@ MapIndexed[(2 Boole[First@ #2 == 1] - 1) n^#1 &, Reverse@ Range@ 4], {n, 0, 33}] (* Michael De Vlieger, Jan 21 2017 *)

Crossrefs

Sequence in context: A215049 A087541 A153434 * A264516 A271845 A348226

Adjacent sequences: A152013 A152014 A152015 * A152017 A152018 A152019

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, Nov 20 2008

Extensions

Offset changed by Bruno Berselli, Jul 27 2012

Status

approved