OFFSET
0,2
COMMENTS
a(n) = number of different substrings of length n found in Kolakoski sequence A000002. It is conjectured that a(n) grows like n^(log(3)/log(3/2)).
REFERENCES
M. Dekking: "What is the long range order in the Kolakoski sequence?" in: The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer, Dordrecht (1997), pp. 115-125.
LINKS
D. Wilson, Table of n, a(n) for n = 0..100.
EXAMPLE
For length 3 only the strings 112, 121, 211, 221, 212, 122 occur, so a(3) = 6. For length 4 only the 10 strings 1121, 1122, 1211, 1212, 1221, 2112, 2121, 2122, 2211, 2212 occur.
MATHEMATICA
nMax = 52; A007782[m_] := A007782[m] = (kolak = {1, 2, 2}; For[n = 3, n <= m, n++, For[k = 1, k <= kolak[[n]], k++, AppendTo[ kolak, 1 + Mod[n - 1, 2]]]]; factors[n_] := Table[ kolak[[k ;; k + n - 1]], {k, 1, Length[kolak] - n + 1}]; Table[ factors[n] // Union // Length, {n, 0, nMax}]); A007782[nMax]; A007782[m = 2*nMax]; While[ A007782[m] != A007782[m/2], m = 2*m]; A007782[m] (* Jean-François Alcover, Jul 24 2013 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Patricia Lamas (lamas(AT)math.uqam.ca)
EXTENSIONS
Additional comments from Michael Baake (mbaake(AT)pion09.tphys.physik.uni-tuebingen.de), Feb 19, 2001.
STATUS
approved