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A007782
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Number of factors in the infinite word formed by the Kolakoski sequence A000002.
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1
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1, 2, 4, 6, 10, 14, 18, 26, 34, 42, 50, 62, 78, 94, 110, 126, 142, 162, 186, 218, 250, 282, 314, 346, 378, 410, 446, 486, 534, 590, 654, 718, 782, 846, 910, 974, 1038, 1102, 1166, 1234, 1302, 1378, 1458, 1554, 1658, 1774, 1898, 2026, 2154, 2282, 2410, 2538, 2666
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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)).
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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.
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LINKS
| D. Wilson, Table of n, a(n) for n=0,...,100.
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EXAMPLE
| For length 3 only the strings 11, 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.
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CROSSREFS
| Sequence in context: A024518 A128422 A098380 * A035501 A024204 A036641
Adjacent sequences: A007779 A007780 A007781 * A007783 A007784 A007785
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KEYWORD
| nonn,nice
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AUTHOR
| Patricia Lamas (lamas(AT)math.uqam.ca)
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EXTENSIONS
| Additional comments from Michael Baake (mbaake(AT)pion09.tphys.physik.uni-tuebingen.de), Feb 19, 2001.
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