This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A318190 #18 Sep 08 2022 08:46:22 %S A318190 0,1,-1,3,5,-1,-7,13,3,5,7,3,17,-5,-31,45,39,-23,-33,51,37,-17,-23,45, %T A318190 11,13,23,3,65,-37,-127,157,79,-47,-1,35,101,-65,-167,205,131,-91,-57, %U A318190 99,145,-101,-191,237,215,-167,-193,243,197,-145,-151,205,75,-19,55,3,257,-197,-511,573,415,-351,-257,323,325 %N A318190 a(0) = 0, a(1) = 1; for n >= 1, a(2*n) = a(2*n-1) - 2*a(n), a(2*n+1) = 2*n - a(2*n). %H A318190 Altug Alkan, <a href="/A318190/b318190.txt">Table of n, a(n) for n = 0..10000</a> %H A318190 Altug Alkan, <a href="/A318190/a318190.png">A scatterplot of a(n) for n <= 10^5</a> %F A318190 G.f. g(x) satisfies g(x) = (x+x^5)/(1-x^2)^2 - x*g(-x) - 2*g(x^2). - _Robert Israel_, Aug 28 2018 %p A318190 f:= proc(n) option remember; %p A318190 if n::even then procname(n-1) - 2*procname(n/2) %p A318190 else n-1-procname(n-1) %p A318190 fi %p A318190 end proc: %p A318190 f(0):= 0: f(1):= 1: %p A318190 map(f, [$0..100]); # _Robert Israel_, Aug 28 2018 %t A318190 a[0]=0; a[1]=1; a[n_] := a[n] = If[EvenQ[n], a[n-1] - 2 a[n/2], n-1 - a[n - 1]]; Array[a, 70, 0] (* _Giovanni Resta_, Aug 27 2018 *) %o A318190 (PARI) a(n)=if(n<=1, n, if(n%2==0, a(n-1)-2*a(n/2), n-1-a(n-1))); %o A318190 (PARI) a = vector(99); print1 (0", "); for(n=1, #a, print1 (a[n]=if(n==1, 1, if(n%2, n-1-a[n-1], a[n-1]-2*a[n/2]))", ")); %o A318190 (Magma) [0] cat [n eq 1 select 1 else n mod 2 eq 0 select Self(n-1)-2*Self(n div 2) else n-1 - Self(n-1): n in [1..70]]; // _Vincenzo Librandi_, Aug 28 2018 %Y A318190 Cf. A002487, A303404. %K A318190 sign,easy,look %O A318190 0,4 %A A318190 _Altug Alkan_, Aug 20 2018