|
| |
|
|
A154955
|
|
a(1)=1, a(2)=-1, followed by 0,0,0...
|
|
6
| |
|
|
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; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Matrix inverse of A000012.
Moebius transform of the sequence A000035=(0,1,0,1,...). Dirichlet inverse of A036987(n-1). 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). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 21 2009]
The Kn21 sums, see A180662, of triangle A108299 equal the terms of this sequence. [Johannes W. Meijer, Aug 14 2011]
|
|
|
FORMULA
| a(n)={C[2*(n-1),n-1] mod 2}-[C(n^2,n+2) mod 2], with n>=1 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 22 2009]
|
|
|
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 (jaroslav.krizek(AT)atlas.cz), Mar 21 2009]
Sequence in context: A134323 A060576 A019590 * A014040 A014071 A014038
Adjacent sequences: A154952 A154953 A154954 * A154956 A154957 A154958
|
|
|
KEYWORD
| sign,tabl
|
|
|
AUTHOR
| Mats Granvik (mats.granvik(AT)abo.fi), Jan 18 2009
|
| |
|
|
