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A163540 The absolute direction (0=east, 1=south, 2=west, 3=north) taken by the type I Hilbert's Hamiltonian walk A163357 at the step n. 9
0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 0, 1, 0, 3, 0, 0, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 1, 0, 3, 0, 0, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 2, 2, 3, 0, 3, 3, 2, 1, 2, 3, 2, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 0, 1, 2, 1, 0, 1, 2, 2, 3, 2, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 3, 2, 3, 0, 0, 0, 1, 2, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Taking every sixteenth term gives the same sequence: (and similarly for all higher powers of 16 as well): a(n) = a(16*n).

LINKS

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

FORMULA

a(n) = A010873(A163538(n)+A163539(n)+abs(A163539(n))+3).

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[FoldList[Mod[Plus[#1, #2], 4] &, 0,

  a[#] & /@ Range[4^4] /. {F[n_] :> 0, L[n_] :> 1, R[n_] :> -1}],

2 ;; -1] (* Bradley Klee, Aug 07 2015 *)

PROG

(Scheme:) (define (A163540 n) (modulo (+ 3 (A163538 n) (A163539 n) (abs (A163539 n))) 4))

CROSSREFS

a(n) = A163540(A008598(n)) = A004442(A163541(n)). See also A163542.

Sequence in context: A065715 A180984 A051628 * A127967 A147602 A114206

Adjacent sequences:  A163537 A163538 A163539 * A163541 A163542 A163543

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 01 2009

STATUS

approved

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Last modified August 4 15:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)