A154955 a(1) = 1, a(2) = -1, followed by 0, 0, 0, ... .

1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Mats Granvik, Jan 18 2009

Keywords

• mult
• sign
• easy

Comments

Matrix inverse of A000012.

Moebius transform of the sequence A000035. Dirichlet inverse of A209229. Partial sums of a(n) is characteristic function of 1 (A063524). a(n)=(-1)^(n+1)*A019590(n). a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), a(n) = Sum_{d|n} b(d)*c(n/d): a(n) = A000012(n) * A092673(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000012(n) = A000035(n), a(n) * A000027(n) = A026741(n), a(n) * A008683(n) = A092673(n), a(n) * A036987(n-1) = A063524(n), a(n) * A000005(n) = A001227(n). - Jaroslav Krizek, Mar 21 2009

The Kn21 sums, see A180662, of triangle A108299 equal the terms of this sequence. - Johannes W. Meijer, Aug 14 2011

{a(n-1)}A132393.%20-%20_Wolfdieter%20Lang">{n>=1}, gives the alternating row sums of A132393. - _Wolfdieter Lang, May 09 2017

With offset 0 the alternating row sums of A097805. - Peter Luschny, Sep 07 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A019590 (absolute values).

Cf. A000005, A000012, A000027, A000035, A001227, A008683, A019590, A026741, A036987, A063524, A092673.

Cf. A097805, A108299, A132393, A180662.

Programs

Mathematica

Join[{1, -1}, 0 Range[3, 100]] (* Wesley Ivan Hurt, Jun 22 2024 *)
PadRight[{1,-1},120,0] (* Harvey P. Dale, Dec 10 2024 *)

PARI

A154955(n)=(n==1)-(n==2) \\ M. F. Hasler, Jan 13 2012

Formula

G.f.: A(x) = x - x^2 = x / (1 + x / (1 - x)). - Michael Somos, Jan 03 2013

a(n) = (2/sqrt(3))*sin((2*Pi/3)*n!). - Lorenzo Pinlac, Jan 16 2022

a(n) = [n = 1] - [n = 2], where [] is the Iverson bracket. - Wesley Ivan Hurt, Jun 22 2024

Multiplicative with a(2) = -1, a(2^e) = 0 if e > 1, a(p^e) = 0 if p > 2. - Antti Karttunen, Dec 17 2024

Extensions

Keyword:mult added by Antti Karttunen, Dec 17 2024