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

1,1

Comments

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

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A327688 A055800 A060572 * A358095 A180009 A341907

Adjacent sequences: A163540 A163541 A163542 * A163544 A163545 A163546

Keyword

nonn

Author

Antti Karttunen, Aug 01 2009

Status

approved