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math.NT2011
A Pattern Sequence Approach to Stern's Sequence
Michael Coons, Jeffrey Shallit
Let w be a binary string and let a_w (n) be the number of occurrences of the word w in the binary expansion of n. As usual we let s(n) denote the Stern sequence; that is, s(0)=0, s…
math.NT2011★ 1 cited
A variant of Hofstadter's sequence and finite automata
J. -P. Allouche, J. Shallit
Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is expli…