cp's OEIS Frontend

A303404 a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1) - 2*a(n), a(2*n+1) = n - 2*a(n).

%I A303404 #76 Aug 20 2018 12:11:36
%S A303404 0,1,-1,-1,1,4,6,5,3,2,-6,-3,-15,-6,-16,-3,-9,2,-2,5,17,22,28,17,47,
%T A303404 42,54,25,57,46,52,21,39,34,30,13,17,22,12,9,-25,-14,-58,-23,-79,-34,
%U A303404 -68,-11,-105,-70,-154,-59,-167,-82,-132,-23,-137,-86,-178,-63,-167,-74,-116,-11,-89,-46,-114,-35,-95,-26,-52,9
%N A303404 a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1) - 2*a(n), a(2*n+1) = n - 2*a(n).
%C A303404 Inspired by A002487.
%C A303404 A020714 is generally determinative for block structures of this sequence.
%H A303404 Altug Alkan, <a href="/A303404/b303404.txt">Table of n, a(n) for n = 0..10240</a>
%H A303404 Altug Alkan, <a href="/A303404/a303404_8.png">A scatterplot of a(n) for n <= 5*2^13</a>
%H A303404 Altug Alkan, <a href="/A303404/a303404_9.png">A scatterplot of first differences of a(n) for n <= 5*2^13</a>
%F A303404 G.f. g(x) satisfies g(x) + 2*g(x^2)*(1+x+x^2) = x + x^2 + x^3 + x^4 + 2*x^5. - _Robert Israel_, Aug 20 2018
%p A303404 A[0]:= 0: A[1]:= 1:
%p A303404 for n from 1 to 50 do
%p A303404   A[2*n]:= A[2*n-1]-2*A[n];
%p A303404   A[2*n+1]:= n - 2*A[n]
%p A303404 od:
%p A303404 seq(A[i],i=0..101); # _Robert Israel_, Aug 20 2018
%o A303404 (PARI) a(n)=if(n<=1, n, if(n%2==0, a(n-1)-2*a(n/2), (n-1)/2-2*a((n-1)/2)));
%Y A303404 Cf. A002487, A305299.
%K A303404 sign,look
%O A303404 0,6
%A A303404 _Altug Alkan_, Aug 19 2018