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A282133 Number of maximal cubefree binary words of length n. 5
0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 10, 12, 14, 28, 38, 56, 84, 124, 184, 264, 374, 544, 836, 1190, 1746, 2544, 3712, 5410, 7890, 11470, 16666, 24436 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

A word is cubefree if it has no block within it of the form xxx, where x is any nonempty block.  A cubefree word w is maximal if it cannot be extended to the right (i.e., both w0 and w1 end in cubes).

It appears that a(n) ~ A028445(n-11). - M. F. Hasler, May 05 2017

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

For n = 8, the two maximal cubefree words of length 8 are 00100100 and its complement 11011011.

The first few maximnal cubefree words beginning with 1 are:

[1, 1, 0, 1, 1, 0, 1, 1],

[1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0],

[1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],

[1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0],

[1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],

[1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0],

[1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0],

[1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1],

[1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1],

[1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]].

For those beginning with 0, take the complements. - N. J. A. Sloane, May 05 2017

MAPLE

# Maple code adapted from that in A286262 by N. J. A. Sloane, May 05 2017

isCubeFree:=proc(v) local n, L;

for n from 3 to nops(v) do for L to n/3 do

if v[n-L*2+1 .. n] = v[n-L*3+1 .. n-L] then RETURN(false) fi od od; true end;

A282133:=proc(n) local s, m;

s:=0;

for m from 2^(n-1) to 2^n-1 do

if isCubeFree(convert(m, base, 2)) then

   if (not isCubeFree(convert(2*m, base, 2))) and

   (not isCubeFree(convert(2*m+1, base, 2))) then

   s:=s+2; fi;

fi;

od; s; end;

[seq(A282133(n), n=0..18)];

CROSSREFS

Cf. A028445, A282317.

For these numbers halved, see A286270.

Sequence in context: A033737 A033747 A087611 * A153869 A128541 A122908

Adjacent sequences:  A282130 A282131 A282132 * A282134 A282135 A282136

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Feb 06 2017

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)