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A285831
Triangular array: row n shows the n+1 zero-one subwords of length n that occur in the infinite Fibonacci word A003849, in lexicographic order.
2
0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0
OFFSET
1
COMMENTS
Exactly n+1 zero-one-words of length n occur as subwords of the infinite Fibonacci word w = A003849 = 01001010010010100101... For n = 0..5, they are listed here in lexicographic order. (See A285830 for a listing in order of appearance in w.)
n subwords of w
0 the empty word
1 0, 1
2 00, 01, 10
3 001, 010, 100, 101
4 0010, 0100, 0101, 1001, 1010
5 00100, 00101, 01001, 01010, 10010, 10100
EXAMPLE
Starting with n=1, take in order the zeros and ones in the triangle of words shown in Comments: 0, 1, 00, 01, 10, 001, 010, 100, 101, ...; represent these as 0,1,0,0,0,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,...
MATHEMATICA
s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 10] (* A003849 *)
(w = Table[DeleteDuplicates[Partition[s, k, 1]], {k, Floor[Length[s/2]]}]) // ColumnForm (* A285830, array *)
Map[Sort, w] // ColumnForm (* A285831, array *)
w1 = Map[Sort, w] ;
Flatten[w] (* A285830, sequence *)
Flatten[w1] (* A285831, sequence *)
(* Peter J. C. Moses, Apr 26 2017 *)
CROSSREFS
Cf. A285830.
Sequence in context: A286052 A342910 A341258 * A188294 A079101 A334941
KEYWORD
nonn,easy,tabf
AUTHOR
Clark Kimberling, May 02 2017
STATUS
approved