A178536 First column of A178535.

1, -2, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0

Offset: 1

Author

Mats Granvik, May 29 2010

Keywords

• sign

Comments

Except for the second term, a(n) seems to be equal to the Mobius function mu(n) = A008683(n) (verified for the first 53 terms).

a(n) = A008683(n) has now been verified for 3 <= n <= 800. - R. J. Mathar, Sep 14 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..800 (prepared from the b-file of A008683 based on _R. J. Mathar_'s Sep 14 2017 comment)

Crossrefs

Cf. A178535, A008683.

Cf. also A181434, A181435.

Programs

Maple

A178536 := proc(n) A178535(n,1) ; end proc;
seq(A178536(n),n=1..80) ; # R. J. Mathar, Oct 28 2010

Mathematica

Clear[t, n, k, nn, a, A]; nn=92; a = Fibonacci[Range[nn] + 1]; t[n_, 1] = If[n >= 1, a[[n]], 0]; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] - Sum[t[n - i, k], {i, 1, k - 1}], 0]; MatrixForm[A = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]; Inverse[A][[All, 1]] (* Mats Granvik, Sep 15 2017 *)

Formula

a(n) = A178535(n,1).

a(n) = Sum_{k|n} A008683(n/k)*([k = 1] - [2|k]) (conjecture). - Mats Granvik, Jan 24 2021

Extensions

More terms from R. J. Mathar, Oct 28 2010