cp's OEIS Frontend

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

%I A081729 #17 Jan 17 2023 14:46:59
%S A081729 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,
%T A081729 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,
%U A081729 -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
%N A081729 Expansion of Sum(k>=0, x^(2^k)) + 1/(1+x). First differences of A007456 (gossip sequence) for n>1.
%C A081729 For n>1: a(n) = 2, if n is power of 2; a(n) =- 1, if n odd; a(n) = 1 otherwise.
%C A081729 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
%H A081729 Antti Karttunen, <a href="/A081729/b081729.txt">Table of n, a(n) for n = 0..65536</a>
%F A081729 a(n) = A209229(n) + A033999(n). - _Reinhard Zumkeller_, Apr 03 2014
%t A081729 Join[{1,0},Table[Which[IntegerQ[Log2[n]],2,OddQ[n],-1,True,1],{n,2,90}]] (* _Harvey P. Dale_, Jan 17 2023 *)
%o A081729 (Haskell)
%o A081729 a081729 n = a209229 n + a033999(n)
%o A081729 -- _Reinhard Zumkeller_, Apr 03 2014
%Y A081729 Cf. A033999, A043529, A160464, A209229.
%K A081729 sign,easy
%O A081729 0,3
%A A081729 _Ralf Stephan_, Apr 06 2003
%E A081729 Erroneous formula removed by _Antti Karttunen_, Sep 14 2017