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 A144595 Christoffel word of slope 4/7. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). REFERENCES J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008. LINKS FORMULA 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] MAPLE 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); CROSSREFS Sequence in context: A131531 A144604 A022926 * A072785 A074937 A143518 Adjacent sequences:  A144592 A144593 A144594 * A144596 A144597 A144598 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 13 2009 STATUS approved

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Last modified May 22 13:06 EDT 2013. Contains 225537 sequences.