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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, 35574, 51892, 75552, 110124, 160624, 234162, 341178, 497058, 725026, 1056630, 1540158, 2244566, 3271600 (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 Lars Blomberg, Table of n, a(n) for n = 1..59 EXAMPLE For n = 8, the two maximal cubefree words of length 8 are 00100100 and its complement 11011011. The first few maximal 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 * A338819 A153869 A128541 Adjacent sequences:  A282130 A282131 A282132 * A282134 A282135 A282136 KEYWORD nonn AUTHOR Jeffrey Shallit, Feb 06 2017 EXTENSIONS a(36)-a(48) from Lars Blomberg, Feb 09 2019 STATUS approved

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Last modified August 4 02:24 EDT 2021. Contains 346441 sequences. (Running on oeis4.)