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A005819 Number of words of length n in a certain language.
(Formerly M1584)
10
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; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. Dulucq and D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990), 381-400.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008, Table of n, a(n) for n = 1..100

S. Dulucq, Etude combinatorie de problemes d'enumeration, d'algorithmique sure les arbres et de codage par des mots, a thesis presented to L'Universite De Bordeaux I, 1987. (Annotated scanned copy)

FORMULA

a(n) = -1 + Sum_{i=1..n} (n-i+1)*phi(i) 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

PROG

(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

CROSSREFS

Sequence in context: A147623 A232234 A045964 * A168193 A182977 A116658

Adjacent sequences:  A005816 A005817 A005818 * A005820 A005821 A005822

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane and Simon Plouffe

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

STATUS

approved

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Last modified October 23 14:53 EDT 2017. Contains 293789 sequences.