

A071160


Łukasiewicz words that are also valid asynchronic siteswap juggling patterns.


4



0, 1, 20, 11, 300, 201, 120, 111, 4000, 3001, 2020, 2011, 1300, 1201, 1120, 1111, 50000, 40001, 30020, 30011, 20300, 20201, 20120, 20111, 14000, 13001, 12020, 12011, 11300, 11201, 11120, 11111, 600000, 500001, 400020, 400011, 300300
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OFFSET

0,3


COMMENTS

Note: this finite decimal representation works only up to the 511th term, as the 512th such word is already (10,0,0,0,0,0,0,0,0,0). The sequence A071161 shows the initial portion of this sequence sorted.


LINKS

Table of n, a(n) for n=0..36.
Peter J. Beek and Arthur Lewbel, The Science of Juggling, Scientific American, Nov, 1995, Vol. 273, Number 5, pp. 9297.
Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507  519.
Juggling Information Service, Site Swap FAQs
A. Karttunen, Gatomorphisms and other excursions amidst the plane trees and parenthesizations (Includes the complete Scheme program for computing this sequence)
R. P. Stanley, Hipparchus, Plutarch, Schröder and Hough, Am. Math. Monthly, Vol. 104, No. 4, p. 344, 1997.
OEIS Wiki, Łukasiewicz words
Index entries for sequences related to Łukasiewicz


FORMULA

Construction: starting from the most significant (the leftmost) bit, replace each 1bit in the binary expansion of n with the distance to the next 1bit to the right, allowing a cyclic wrapover from the leastsignificant 1bit to the most significant 1bit. I.e. from 22 = 10110 in binary we get 20120, the 22nd term of this sequence.
a(n) = A071161(A054429(n)).


CROSSREFS

Subset of A071153.
Cf. A060495, A060498, A065177, A071162, A071163.
Sequence in context: A058282 A298208 A247337 * A071153 A209644 A154043
Adjacent sequences: A071157 A071158 A071159 * A071161 A071162 A071163


KEYWORD

nonn,fini


AUTHOR

Antti Karttunen, May 14 2002


STATUS

approved



