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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

FORMULA

a(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 *)