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A152015 n^3-n^2-n. 4
0, -1, 2, 15, 44, 95, 174, 287, 440, 639, 890, 1199, 1572, 2015, 2534, 3135, 3824, 4607, 5490, 6479, 7580, 8799, 10142, 11615, 13224, 14975, 16874, 18927, 21140, 23519, 26070, 28799, 31712, 34815, 38114, 41615, 45324, 49247, 53390, 57759, 62360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n > 1, these are also the largest positive integers k such that k + n divides k^3 + n^2. For all n > 1 and p > 1, the largest positive integer k such that k + n divides k^p + n^(p-1) is given by k = n^p - (-n)^(p-1) - n. Here, p = 3. - Derek Orr, Aug 13 2014

LINKS

Derek Orr, Table of n, a(n) for n = 0..10000

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

FORMULA

G.f.: -x*(1-6*x-x^2)/(1-x)^4. - Bruno Berselli, Jul 27 2012

a(n) = A002414(n) - A005449(n). - Wesley Ivan Hurt, Oct 06 2013

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, Aug 13 2014

MAPLE

a:=n->sum(-1+sum(1+sum(1, i=2..n), j=2..n), k=1..n): seq(a(n), n=0..44); # [Zerinvary Lajos, Dec 22 2008]

A152015:=n->n^3-n^2-n: seq(A152015(k), k=0..100); # Wesley Ivan Hurt, Oct 06 2013

MATHEMATICA

lst={}; Do[AppendTo[lst, n^3-n^2-n], {n, 0, 5!}]; lst

Table[n^3-n^2-n, {n, 0, 100}] (* Wesley Ivan Hurt, Oct 06 2013 *)

PROG

(PARI) vector(100, n, (n-1)^3-(n-1)^2-(n-1)) \\ Derek Orr, Aug 13 2014

(MAGMA) [n^3-n^2-n : n in [0..50]]; // Wesley Ivan Hurt, Aug 13 2014

CROSSREFS

Cf. A002414, A005449.

Sequence in context: A254856 A001007 A300393 * A318914 A162256 A229013

Adjacent sequences:  A152012 A152013 A152014 * A152016 A152017 A152018

KEYWORD

sign,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Nov 20 2008

EXTENSIONS

Offset changed by Bruno Berselli, Jul 27 2012

STATUS

approved

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Last modified October 20 04:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)