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A163543 The relative direction (0=straight ahead, 1=turn right, 2=turn left) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.

%I A163543 #12 Jul 03 2025 20:39:14
%S A163543 2,2,1,0,1,1,2,2,1,1,0,1,2,2,0,2,1,1,2,0,2,2,1,1,2,2,0,2,1,1,0,0,1,1,
%T A163543 2,0,2,2,1,1,2,2,0,2,1,1,2,0,2,2,1,0,1,1,2,2,1,1,0,1,2,2,1,0,1,1,2,0,
%U A163543 2,2,1,1,2,2,0,2,1,1,0,1,2,2,1,0,1,1,2,2,1,1,0,1,2,2,0,0,2,2,1,0,1,1
%N A163543 The relative direction (0=straight ahead, 1=turn right, 2=turn left) taken by the type I Hilbert's Hamiltonian walk A163359 at the step n.
%C A163543 a(16*n) = a(256*n) for all n.
%H A163543 A. Karttunen, <a href="/A163543/b163543.txt">Table of n, a(n) for n = 1..4096</a>
%F A163543 a(n) = A163241((A163541(n+1)-A163541(n)) modulo 4).
%t A163543 HC = {
%t A163543 L[n_ /; IntegerQ[n/2]] :> {F[n], L[n], L[n + 1], R[n + 2]},
%t A163543 R[n_ /; IntegerQ[(n + 1)/2]] :> {F[n], R[n], R[n + 3], L[n + 2]},
%t A163543 R[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], F[n + 3]},
%t A163543 L[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], F[n + 1]},
%t A163543 F[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], L[n + 3]},
%t A163543 F[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], R[n + 1]}};
%t A163543 a[1] = F[0]; Map[(a[n_ /; IntegerQ[(n - #)/16] ] := Part[Flatten[a[(n + 16 - #)/16] /. HC /. HC],#]) &, Range[16]];
%t A163543 Part[a[#] & /@ Range[4^4] /. {L[_] -> 2, R[_] -> 1, F[_] -> 0}, 2 ;; -1] (* _Bradley Klee_, Aug 06 2015 *)
%o A163543 (Scheme) (define (A163543 n) (A163241 (modulo (- (A163541 (1+ n)) (A163541 n)) 4)))
%Y A163543 a(n) = A014681(A163542(n)). See also A163541.
%K A163543 nonn
%O A163543 1,1
%A A163543 _Antti Karttunen_, Aug 01 2009