0,1

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).

J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008.

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 (ppl(AT)spl.at), Jan 19 2009]

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);

Sequence in context: A131531 A144604 A022926 this_sequence A072785 A074937 A143518

Adjacent sequences: A144592 A144593 A144594 this_sequence A144596 A144597 A144598

nonn

N. J. A. Sloane (njas(AT)research.att.com), Jan 13 2009