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URL: https://oeis.org/A372846

⇱ A372846 - OEIS


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A372846
a(n) is the number of states in the smallest deterministic finite automaton that accepts the Zeckendorf representation of i and n*i, in parallel, for all integers i>=0.
0
2, 10, 23, 40, 59, 85, 114, 146, 181, 224, 269, 318, 371, 429, 489, 552, 621, 695, 771, 850, 935, 1024, 1115, 1213, 1314, 1418, 1525, 1640, 1757, 1878, 2003, 2132, 2264, 2399, 2541, 2686, 2834, 2985, 3143, 3303, 3467, 3636, 3809, 3985, 4164, 4350, 4539, 4731
OFFSET
1,1
COMMENTS
Conjecture: a(n) <= 2*n^2 + g^2*n + 1, where g = (1+sqrt(5))/2.
LINKS
Delaram Moradi, Narad Rampersad, and Jeffrey Shallit, Complexity of Linear Subsequences of Fibonacci-Automatic Sequences, arXiv:2603.21645 [cs.FL], 2026. See p. 12.
CROSSREFS
Sequence in context: A333703 A120548 A284360 * A255606 A293403 A316451
KEYWORD
nonn,changed
AUTHOR
Jeffrey Shallit, Jul 04 2024
STATUS
approved