

A282949


Number of distinct subword complexity profiles for binary strings of length n.


1



1, 2, 2, 3, 4, 5, 7, 9, 13, 18, 25, 34, 48, 67, 97, 134, 191, 258, 374, 521, 738, 1024, 1431, 1972, 2755, 3785, 5244, 7223, 9937, 13545, 18597, 25360, 34500
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OFFSET

1,2


COMMENTS

The subword complexity function p_i(w) maps i to the number of distinct contiguous blocks (aka subwords, aka factors) of length i in a word w. The subword complexity profile of a word of length n is the list (p_1 (w), p_2 (w), ..., p_n (w)).


LINKS

Table of n, a(n) for n=1..33.


EXAMPLE

For n = 6 the 5 distinct profiles are (1,1,1,1,1,1) (for the word 000000); (2,2,2,2,2,1) (for the word 000001); (2,3,3,3,2,1) (for the word 000010); (2,3,4,3,2,1) (for the word 000100); and (2,4,4,3,2,1) (for the word 000110).


MATHEMATICA

prof[w_] := Table[ Length@ Union@ Partition[w, k, 1], {k, Length@w}]; a[n_] := Length@ Union[prof /@ Tuples[{0, 1}, n]]; Array[a, 12] (* Giovanni Resta, Feb 25 2017 *)


CROSSREFS

Sequence in context: A205579 A089047 A133498 * A292200 A249576 A097600
Adjacent sequences: A282946 A282947 A282948 * A282950 A282951 A282952


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Feb 25 2017


EXTENSIONS

a(26)a(33) from Lars Blomberg, Mar 13 2017


STATUS

approved



