A163542 The relative direction (0=straight ahead, 1=turn right, 2=turn left) taken by the type I Hilbert's Hamiltonian walk A163357 at the step n.

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, 2, 2, 1, 1, 0, 1, 2, 2, 1, 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, 0, 2, 1, 1, 2, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 1, 0, 0, 1, 1, 2, 0, 2, 2

Offset

1,3

Comments

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

Links

A. Karttunen, Table of n, a(n) for n = 1..65536

Formula

a(n) = A163241((A163540(n+1)-A163540(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] = L[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 07 2015 *)

Prog

(Scheme:) (define (A163542 n) (A163241 (modulo (- (A163540 (1+ n)) (A163540 n)) 4)))

Crossrefs

a(n) = A014681(A163543(n)). See also A163540.

Sequence in context: A344319 A236998 A297116 * A061895 A129678 A261773

Adjacent sequences: A163539 A163540 A163541 * A163543 A163544 A163545

Keyword

nonn

Author

Antti Karttunen, Aug 01 2009

Status

approved