A308343 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.

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

Offset: 1

Author

Rémy Sigrist, May 21 2019

Keywords

• sign

Examples

			The first terms, alongside the numbers of zeros and of ones and A038219(n), are:
  n   a(n)  #0's  #1's  A038219(n)
  --  ----  ----  ----  ----------
   1     1     1     0           0
   2     0     1     1           1
   3     1     2     1           0
   4     2     3     1           0
   5     1     3     2           1
   6     0     3     3           1
   7     1     4     3           0
   8     0     4     4           1
   9     1     5     4           0
  10     0     5     5           1
  11    -1     5     6           1
  12    -2     5     7           1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 500000 terms
• Rémy Sigrist, Perl program for A308343

Crossrefs

Cf. A038219.

Programs

Perl

See Links section.

Formula

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