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).

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

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