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.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Aug 01 2009

Keywords

• nonn

Comments

a(16*n) = a(256*n) for all n.

Links

• A. Karttunen, Table of n, a(n) for n = 1..4096

Crossrefs

a(n) = A014681(A163542(n)). See also A163541.

Programs

Mathematica

HC = {
L[n_ /; IntegerQ[n/2]] :> {F[n], L[n], L[n + 1], R[n + 2]},
R[n_ /; IntegerQ[(n + 1)/2]] :> {F[n], R[n], R[n + 3], L[n + 2]},
R[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], F[n + 3]},
L[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], F[n + 1]},
F[n_ /; IntegerQ[n/2]] :> {L[n], R[n + 1], R[n], L[n + 3]},
F[n_ /; IntegerQ[(n + 1)/2]] :> {R[n], L[n + 3], L[n], R[n + 1]}};
a[1] = F[0]; Map[(a[n_ /; IntegerQ[(n - #)/16] ] := Part[Flatten[a[(n + 16 - #)/16] /. HC /. HC],#]) &, Range[16]];
Part[a[#] & /@ Range[4^4] /. {L[] -> 2, R[] -> 1, F[] -> 0}, 2 ;; -1] (* _Bradley Klee, Aug 06 2015 *)

Scheme

(define (A163543 n) (A163241 (modulo (- (A163541 (1+ n)) (A163541 n)) 4)))

Formula

a(n) = A163241((A163541(n+1)-A163541(n)) modulo 4).