A308343 - OEIS

%I #11 May 22 2019 03:36:07

%S 1,0,1,2,1,0,1,0,1,0,-1,-2,-1,0,1,0,1,2,3,4,3,2,1,0,1,0,-1,0,1,0,1,0,

%T 1,2,1,2,3,2,1,0,1,0,1,2,3,2,1,2,3,4,5,6,5,6,5,4,5,4,3,2,1,0,1,2,1,0,

%U 1,2,1,0,-1,-2,-3,-4,-3,-4,-3,-4,-3,-4,-5,-4

%N a(n) is the difference between the number of zeros and the number of ones among the first n terms of the Ehrenfeucht-Mycielski sequence A038219.

%H Rémy Sigrist, <a href="/A308343/b308343.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A308343/a308343.png">Scatterplot of the first 500000 terms</a>

%H Rémy Sigrist, <a href="/A308343/a308343.pl.txt">Perl program for A308343</a>

%F a(n) = Sum_{k = 1..n} (-1)^A038219(k).

%e The first terms, alongside the numbers of zeros and of ones and A038219(n), are:

%e   n   a(n)  #0's  #1's  A038219(n)

%e   --  ----  ----  ----  ----------

%e    1     1     1     0           0

%e    2     0     1     1           1

%e    3     1     2     1           0

%e    4     2     3     1           0

%e    5     1     3     2           1

%e    6     0     3     3           1

%e    7     1     4     3           0

%e    8     0     4     4           1

%e    9     1     5     4           0

%e   10     0     5     5           1

%e   11    -1     5     6           1

%e   12    -2     5     7           1

%o (Perl) See Links section.

%Y Cf. A038219.

%K sign

%O 1,4

%A _Rémy Sigrist_, May 21 2019