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A154955 a(1) = 1, a(2) = -1, followed by 0, 0, 0, ... . 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)}_{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

Table of n, a(n) for n=1..105.

FORMULA

a(n) = {C[2*(n-1),n-1] mod 2}-[C(n^2,n+2) mod 2], with n>=1. - Paolo P. Lava, Jan 22 2009

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

a(n) = (1 + sign((5/2) - n))*(-1)^(n + 1)/2. - Wesley Ivan Hurt, Jun 20 2014

a(n) = floor( 1/(n - sign(n-1)) )*(-1)^(n + 1). - Wesley Ivan Hurt, Jun 20 2014

PROG

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

CROSSREFS

Cf. A000035, A036987, A063524, A019590, A000012, A000027, A026741, A008683, A092673, A000005, A001227. [From Jaroslav Krizek, Mar 21 2009]

Cf. A132393.

Sequence in context: A060576 A261012 A019590 * A014040 A014071 A014038

Adjacent sequences:  A154952 A154953 A154954 * A154956 A154957 A154958

KEYWORD

sign,easy

AUTHOR

Mats Granvik, Jan 18 2009

STATUS

approved

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.