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A049538
Number of distinct binary sequences that can be generated by a general (non-linear) binary feedback shift register of length n, but not by a shorter one.
1
1, 2, 10, 105, 3823, 2218961
OFFSET
0,2
COMMENTS
Complementary sequences (e.g.: 111010 and 000101) are taken to be equivalent. Related to maximum order complexity of sequences and also to number of incomplete paths in a De Bruijn graph.
LINKS
C. J. A. Jansen, Investigations on Nonlinear Streamcipher Systems: Construction and Evaluation Methods, Ph.D. Thesis, Delft University of Technology, The Netherlands, 1989, pp. 58-81.
EXAMPLE
For n <= 2, the following sequences can be generated. The periodic part is shown in square brackets. Only sequences starting with 0 are shown, since complementary sequences are equivalent.
n | sequences
-------------
0 | [0]
-------------
1 | [01]
| 0[1]
-------------
2 | [001]
| 0[01]
| [0011]
| 0[011]
| 00[1]
| 01[0]
| [010]
| 011[0]
| [0110]
| [011]
CROSSREFS
Cf. A049539.
Sequence in context: A273965 A273961 A365507 * A217901 A127728 A306064
KEYWORD
nonn,more
AUTHOR
Cees J. A. Jansen (cja(AT)iae.nl)
EXTENSIONS
Name clarified, and a(5) from Pontus von Brömssen, Jan 12 2023
STATUS
approved