A059261 Hilbert's Hamiltonian walk on N X N projected onto the first diagonal: M(3) (sum of the sequences A059252 and A059253).

0, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 8, 7, 6, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 12, 11, 10, 11, 10, 9, 8, 9, 8, 7, 6, 7, 6, 5, 4, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 12, 11, 10, 11, 12, 13, 14, 13, 14, 15

Offset

0,3

Comments

The interest comes from a simplest recursion than the cross-recursion, dependent on parity, governing the projections onto the x and y axis.

Links

A. Karttunen, Table of n, a(n) for n = 0..65535

Formula

Initially, M(0)=0; recursion: M(n+1)=M(n).f(M(n), n).f(M(n), n+1).d(M(n), n); -f(m, n) is the alphabetic morphism i := i+2^n; [example: f(0 1 2 1 2 3 4 3 4 5 6 5 4 3 2 3, 2)=4 5 6 5 6 7 8 7 8 9 10 9 8 7 6 7 ] -d(m, n) is the complementation to 2^(n-1)*3-2, alphabetic morphism; [example: d(0 1 2 1 2 3 4 3 4 5 6 5 4 3 2 3, 3)=10 9 8 9 8 7 6 7 6 5 4 5 6 7 8 7] Here is M(3). [M(1)=0.1.2.1, M(2)=0 1 2 1.2 3 4 3.4 5 6 5.4 3 2 3]

Crossrefs

Cf. the x-projection m(3), A059252 and the y-projection m'(3), A059253. See also: A163530, A059285, A163547.

Sequence in context: A030330 A286579 A293689 * A285869 A162330 A134967

Adjacent sequences: A059258 A059259 A059260 * A059262 A059263 A059264

Keyword

nonn

Author

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

Extensions

Extended by Antti Karttunen, Aug 01 2009

Status

approved