

A275202


Subword complexity (number of distinct blocks of length n) of the period doubling sequence A096268.


1



2, 3, 5, 6, 8, 10, 11, 12, 14, 16, 18, 20, 21, 22, 23, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 161, 162, 163, 164, 165
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OFFSET

1,1


REFERENCES

HsienKuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wpcontent/files/2016/12/aathhrr1.pdf. Also Exact and Asymptotic Solutions of a DivideandConquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585


LINKS

Table of n, a(n) for n=1..101.
Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.


EXAMPLE

For n = 1 there are two words {0,1}. For n = 2 there are three words {00,01,10}. For n = 3 there are five words {000,001,010,100,101}


MATHEMATICA

t = Nest[Flatten[# /. {0 > {1, 0}, 1 > {0, 0}}] &, {1}, 12]; Table[2^n  Count[SequencePosition[t, #] & /@ Tuples[{0, 1}, n], {}], {n, 16}] (* Michael De Vlieger, Jul 19 2016, Version 10.1, after Robert G. Wilson v at A096268 *)


CROSSREFS

Cf. A096268, A035263.
Sequence in context: A024609 A167056 A131614 * A233592 A320773 A138390
Adjacent sequences: A275199 A275200 A275201 * A275203 A275204 A275205


KEYWORD

nonn


AUTHOR

Daniel Rust, Jul 19 2016


STATUS

approved



