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Search: id:A005819
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| A005819 |
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Number of words of length n in a certain language.
(Formerly M1584)
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+0
1
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| 1, 2, 6, 12, 22, 34, 52, 74, 102, 134, 176, 222, 280, 344, 416, 496, 592, 694, 814, 942, 1082, 1232, 1404, 1584, 1784, 1996, 2226, 2468, 2738, 3016, 3324, 3648, 3992, 4352, 4736, 5132, 5564, 6014, 6488, 6978, 7508, 8050, 8634, 9238, 9866, 10516, 11212
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Dulucq and D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400.
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LINKS
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Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008, Table of n, a(n) for n = 1..100
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FORMULA
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a(n)=-1+sum((n-i+1)phi(i), i=1..n) for n>=2, where phi is Euler's totient function (this is conjectured in the Duluck & Gouyou-Beauchamps paper, p. 399).
J. Berstel and M. Pocchiola. A geometric proof of the enumeration formula for Sturmian words. Internat. J. Algeb. Comput., 3(3):349-355, 1993. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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PROGRAM
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(PARI) a(n)=if(n<2, n>0, sum(i=1, n, (n-i+1)*eulerphi(i))-1) - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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CROSSREFS
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Sequence in context: A126428 A147623 A045964 this_sequence A131520 A086953 A101953
Adjacent sequences: A005816 A005817 A005818 this_sequence A005820 A005821 A005822
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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