This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A288002 #43 Mar 30 2021 01:33:09
%S A288002 0,0,1,0,1,1,2,0,1,1,3,1,2,2,3,0,1,1,4,1,3,3,5,1,2,2,5,2,3,3,4,0,1,1,
%T A288002 5,1,4,4,7,1,3,3,8,3,5,5,7,1,2,2,7,2,5,5,8,2,3,3,7,3,4,4,5,0,1,1,6,1,
%U A288002 5,5,9,1,4,4,11,4,7,7,10,1,3,3,11,3,8,8
%N A288002 L-fusc, sequence l of the mutual diatomic recurrence pair: l(1)=0, r(1)=1, l(2n) = l(n), r(2n) = r(n), l(2n+1) = l(n)+r(n), r(2n+1) = l(n+1)+r(n+1), where r(n) = A288003(n).
%C A288002 Define a sequence chf(n) of Christoffel words over an alphabet {-,+}:
%C A288002 chf(1) = '-',
%C A288002 chf(2*n+0) = negate(chf(n)),
%C A288002 chf(2*n+1) = negate(concatenate(chf(n),chf(n+1))).
%C A288002 Each chf(n) word has the length fusc(n) = A002487(n) and splits uniquely into two parent Christoffel words - the left Christoffel word lef(n) of the length l-fusc(n) = a(n) and the right Christoffel word rig(n) of the length r-fusc(n) = A288003(n). See the example below.
%F A288002 a(n) = A002487(n) - A288003(n). [l-fusc(n) = fusc(n) - r-fusc(n).]
%F A288002 gcd(a(n),A288003(n)) = gcd(a(n),A002487(n)) = 1.
%F A288002 a(n) = A007306(n) - A287896(n).
%F A288002 a(n) = A007306(n) mod A002487(n).
%e A288002 The odd bisection CHF(n) of the chf(n) sequence shifted rightwards by a(n) determines the longest overlap of the adjacent CHF words. Note that the first overlapping letters differ for n == 2^k or equivalently when a(n)==0.
%e A288002 To construct the word CHF(n+1) from the word CHF(n): cut off the word negate(lef(n)) of length a(n) at the left side of CHF(n), add the word negate(rig(n)) of length A288003(n) at the right side of CHF(n) and negate the first letter of the new word iff a(n)==0.
%e A288002 n chf(n) A070939(n) A002487(n) lef(n) a(n) CHF(n)
%e A288002 fusc(n) l-fusc(n) bisection of chf(n)
%e A288002 1 '-' 1 1 '' 0 '-'
%e A288002 2 '+' 2 1 '' 0 '+-'
%e A288002 3 '+-' 2 2 '+' 1 '--+'
%e A288002 4 '-' 3 1 '' 0 '-++'
%e A288002 5 '--+' 3 3 '-' 1 '+++-'
%e A288002 6 '-+' 3 2 '-' 1 '++-+-'
%e A288002 7 '-++' 3 3 '-+' 2 '+-+--'
%e A288002 8 '+' 4 1 '' 0 '+---'
%e A288002 9 '+++-' 4 4 '+' 1 '----+'
%e A288002 10 '++-' 4 3 '+' 1 '---+--+'
%e A288002 11 '++-+-' 4 5 '++-' 3 '--+--+-+'
%e A288002 12 '+-' 4 2 '+' 1 '--+-+-+'
%e A288002 13 '+-+--' 4 5 '+-' 2 '-+-+-++'
%e A288002 14 '+--' 4 3 '+-' 2 '-+-++-++'
%e A288002 15 '+---' 4 4 '+--' 3 '-++-+++'
%e A288002 16 '-' 5 1 '' 0 '-++++'
%e A288002 17 '----+' 5 5 '-' 1 '+++++-'
%o A288002 (Python)
%o A288002 def l(n): return 0 if n==1 else l(n//2) if n%2==0 else l((n - 1)//2) + r((n - 1)//2)
%o A288002 def r(n): return 1 if n==1 else r(n//2) if n%2==0 else l((n + 1)//2) + r((n + 1)//2)
%o A288002 print([l(n) for n in range(1, 151)]) # _Indranil Ghosh_, Jun 11 2017
%Y A288002 Cf. A002487, A070939, A287729, A287730, A288003.
%K A288002 nonn
%O A288002 1,7
%A A288002 _I. V. Serov_, Jun 10 2017