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A144595
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Christoffel word of slope 4/7.
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18
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0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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The Christoffel word (or path) of slope s is defined as follows.
Start at (0,0) in the 2-dimensional integer lattice and move up if possible, otherwise right, always keeping below or on the line y = s*x. Write down 0 with a horizontal move, 1 for a vertical move. The first move is necessarily horizontal, so the sequence always begins with 0.
If s is irrational this is called a Sturmian word.
If the first 9 terms are deleted we get the "Upper Christoffel word of slope 4/7" (see Berstal et al., p. 6, Fig. 2).
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REFERENCES
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J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008.
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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Period 11: 0,0,1,0,0,1,0,0,1,0,1.
a(n)=(1/605)*{59*(n mod 11)-51*[(n+1) mod 11]+59*[(n+2) mod 11]-51*[(n+3) mod 11]+4*[(n+4) mod 11]+59*[(n+5) mod 11]-51*[(n+6) mod 11]+4*[(n+7) mod 11]+59*[(n+8) mod 11]-51*[(n+9) mod 11]+4*[(n+10) mod 11]}, with n>=0 [From Paolo P. Lava, Jan 19 2009]
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MAPLE
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christoffel:=proc(s, M) local n, x, y, ans;
ans:=[0]; x:=1; y:=0;
for n from 1 to M do
if y+1 <= s*x then ans:=[op(ans), 1]; y:=y+1; else ans:=[op(ans), 0]; x:=x+1; fi;
od: ans; end; christoffel(4/7, 120);
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CROSSREFS
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Sequence in context: A131531 A144604 A022926 * A072785 A074937 A143518
Adjacent sequences: A144592 A144593 A144594 * A144596 A144597 A144598
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 13 2009
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STATUS
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approved
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