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A359228 Number of states in the minimal deterministic finite automaton with output generating the n-fold running sum (mod 2) of the Thue-Morse sequence (A010060). 0
2, 8, 16, 12, 32, 24, 19, 28, 64, 48, 38, 36, 34, 29, 48, 52, 128, 96, 76, 72, 74, 54, 56, 52, 64, 53, 48, 41, 84, 64, 83, 108, 256, 192, 152, 144, 146, 108, 110, 100, 144, 114, 96, 74, 102, 78, 82, 84, 120, 96, 87, 76, 86, 71, 66, 61, 154, 120, 94, 84, 138, 109, 176, 212, 512, 384, 304, 288, 292, 216 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The 0-fold running sum of A010060 is A010060. To generate the n-fold running sum {c(k)} from the (n-1)-fold running sum {b(k)}, define c(0) = b(0) and c(k+1) = (c(k) + b(k+1)) mod 2.
LINKS
Table of n, a(n) for n=0..69.
Jeffrey Shallit and Anatoly Zavyalov, Transduction of Automatic Sequences and Applications, arXiv:2303.15203 [cs.FL], 2023, see p. 21.
FORMULA
a(2^n) = 2^(n+3) (Proof in Shallit and Zavyalov). - Anatoly Zavyalov, Mar 30 2023
CROSSREFS
Cf. A010060.
Sequence in context: A094513 A110004 A182039 * A174882 A080095 A193219
Adjacent sequences: A359225 A359226 A359227 * A359229 A359230 A359231
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Dec 22 2022
EXTENSIONS
More terms from Anatoly Zavyalov, Mar 30 2023
STATUS
approved

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Last modified August 31 06:39 EDT 2024. Contains 375552 sequences. (Running on oeis4.)