A001489 a(n) = -n.

0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65

Offset: 0

Author

N. J. A. Sloane

Keywords

• core
• sign
• easy

Comments

Also: the nonpositive integers, listed with offset = 0 and in decreasing order.

An involution: the function is its own inverse, A001489 o A001489 = A001477, the identity function on N = {0, 1, 2, 3, ...}. - M. F. Hasler, Jan 18 2015

Examples

			G.f. = -x - 2*x^2 - 3*x^3 - 4*x^4 - 5*x^5 - 6*x^6 - 7*x^7 - ... - _Michael Somos_, Aug 04 2018
		

Links

• David Wasserman, Table of n, a(n) for n = 0..1000
• D. Dumont and J. Zeng, Polynomes d'Euler et les fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998) 3, 387-410.
• Tanya Khovanova, Recursive Sequences
• A. Randrianarivony and J. Zeng, Une famille de polynomes qui interpole plusieurs suites classiques de nombres, Adv. Appl. Math. 17 (1996), 1-26.
• J. Zeng, Sur quelques propriétés de symétrie des nombres de Genocchi, Discr. Math. 153 (1996) 319-333.
• Index entries for "core" sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Partial sums of A057428.

Programs

Maple

A001489 := n->-n;
[ seq(-n,n=0..100) ];

Mathematica

Table[ -n, {n, 0, 50}] (* Stefan Steinerberger, Apr 01 2006 *)

PARI

a(n)=-n \\ Charles R Greathouse IV, Jun 04 2013

Python

def A001489(n): return -n # Chai Wah Wu, Nov 14 2022

Formula

a(n) = -n.

G.f.: -x/(1-x)^2.

a(n) = -a(-n) for all n in Z. - Michael Somos, Aug 04 2018

Extensions

Edited by M. F. Hasler, Jan 18 2015