A059285 Hilbert's Hamiltonian walk projected onto the second diagonal: M'(3) (difference between sequences A059253 and A059252; their sum is A059261).

0, 1, 0, -1, -2, -3, -2, -1, 0, -1, 0, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 7, 6, 5, 4, 5, 4, 3, 2, 3, 2, 1, 0, -1, 0, 1, 2, 3, 2, 1, 0, 1, 0, -1, -2, -1, -2, -3, -4, -5, -4, -3, -2, -1, -2, -3, -4, -3, -4, -5, -6, -5, -6, -7

Offset

0,5

Links

Table of n, a(n) for n=0..63.

Formula

Initially, M'(0)=0; recursion: M'(2n)=M'(2n-1). (-f(-M'(2n-1), 2n-1)).(-M'(2n-1)).f(M'(2n-1), 2n-1), M'(2n+1)=M'(2n).f(M'(2n), 2n).(-M'(2n)).(-(f(-M'(2n), 2n+1)). f(m, n) is the complementation to 2^n, [example: f(4 3 4 5 6 7 6 5 4 5 4 6 2 3 2 1, 3)=4 5 4 3 2 1 2 3 4 3 4 5 6 5 6 7]; (-m) is the opposite[example: m=4 5 4 3 2 1 2 3 4 3 4 5 6 5 6 7, (-m)=-4 -5 -4 -3 -2 -1 -2 -3 -4 -3 -4 -5 -6 -5 -6 -7] [Corrected by Sean A. Irvine, Sep 17 2022]

Example

[M'(0)=0, M'(1)=0 1 0 -1, M'(2)=0 1 0 -1 -2 -3 -2 -1 0 -1 0 1 2 1 2 3]

Crossrefs

The x-projection m(3) is A059253, the y-projection m(3) is A059252 and the projection onto the first diagonal, M(3), is A059261.

Sequence in context: A122445 A189511 A165592 * A165578 A020990 A260686

Adjacent sequences: A059282 A059283 A059284 * A059286 A059287 A059288

Keyword

sign

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Jan 24 2001

Status

approved