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%I #7 Mar 31 2012 13:21:08
%S 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,
%T 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,
%U 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
%N Hilbert's Hamiltonian walk on N X N projected onto the first diagonal: M(3) (sum of the sequences A059252 and A059253).
%C The interest comes from a simplest recursion than the cross-recursion, dependent on parity, governing the projections onto the x and y axis.
%H A. Karttunen, <a href="/A059261/b059261.txt">Table of n, a(n) for n = 0..65535</a>
%F 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]
%Y Cf. the x-projection m(3), A059252 and the y-projection m'(3), A059253. See also: A163530, A059285, A163547.
%K nonn
%O 0,3
%A Claude Lenormand (claude.lenormand(AT)free.fr), Jan 24 2001
%E Extended by _Antti Karttunen_, Aug 01 2009
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