A081729 Expansion of Sum(k>=0, x^(2^k)) + 1/(1+x). First differences of A007456 (gossip sequence) for n>1.

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

Offset: 0

Author

Ralf Stephan, Apr 06 2003

Keywords

• sign
• easy

Comments

For n>1: a(n) = 2, if n is power of 2; a(n) =- 1, if n odd; a(n) = 1 otherwise.

The absolute values of a(n) for n>=2 equal the q(n) sequence of the Eta triangle A160464. - Johannes W. Meijer, May 24 2009

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65536

Crossrefs

Cf. A033999, A043529, A160464, A209229.

Programs

Haskell

a081729 n = a209229 n + a033999(n)
-- Reinhard Zumkeller, Apr 03 2014

Mathematica

Join[{1,0},Table[Which[IntegerQ[Log2[n]],2,OddQ[n],-1,True,1],{n,2,90}]] (* Harvey P. Dale, Jan 17 2023 *)

Formula

a(n) = A209229(n) + A033999(n). - Reinhard Zumkeller, Apr 03 2014

Extensions

Erroneous formula removed by Antti Karttunen, Sep 14 2017