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A059261 Hilbert's Hamiltonian walk on N X N projected onto the first diagonal: M(3) (sum of the sequences A059252 and A059253). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)