A019311 Number of words of length n (n >= 1) over a two-letter alphabet having a minimal period of size n-2.
0, 0, 2, 2, 6, 12, 28, 48, 106, 198, 414, 800, 1644, 3236, 6546, 12982, 26130, 52048, 104404, 208372, 417390, 833930, 1669102, 3336476, 6675512, 13347600, 26700226, 53393562, 106797302, 213580904, 427181968, 854336432, 1708713470, 3417372070, 6834824970
Offset: 1
Keywords
Examples
a(5) = 6 because we have: {0, 0, 1, 0, 0}, {1, 1, 0, 1, 1}, {0, 1, 0, 0, 1},
{0, 1, 1, 0, 1}, {1, 0, 0, 1, 0}, {1, 0, 1, 1, 0}. The first two words have autocorrelation polynomial equal to 1 + z^3 + z^4, the last four words have autocorrelation polynomial equal to 1 + z^4. - _Geoffrey Critzer_, Apr 13 2022
Links
- H. Harborth, Endliche 0-1-Folgen mit gleichen Teilblöcken, Journal für Mathematik, 271 (1974) 139-154.
- Sean A. Irvine, Java program (github)
Extensions
More terms from Jeffrey Shallit, Feb 20 2013
More terms from Sean A. Irvine, Jun 20 2021