Search: id:A059253
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%I A059253
%S A059253 0,1,1,0,0,0,1,1,2,2,3,3,3,2,2,3,4,4,5,5,6,7,7,6,6,7,7,6,5,5,4,4,4,4,
%T A059253 5,5,6,7,7,6,6,7,7,6,5,5,4,4,3,2,2,3,3,3,2,2,1,1,0,0,0,1,1,0,0,0,1,1,
%U A059253 2,3,3,2,2,3,3,2,1,1,0,0,0,1,1,0,0,0,1,1,2,2,3,3,3,2,2,3,4,5,5,4,4,4
%N A059253 Hilbert's Hamiltonian walk on N X N projected onto y axis: m'(3).
%C A059253 This is the Y-coordinate of the nth term in the type I Hilbert's Hamiltonian 
               walk A163359 and the X-coordinate of its transpose A163357.
%H A059253 A. Karttunen, <a href="b059253.txt">Table of n, a(n) for n = 0..65535</
               a>
%F A059253 Initially [m(0) = 0, m'(0) = 0]; recursion: m(2n + 1) = m(2n).m'(2n).f(m'(2n), 
               2n).c(m(2n), 2n + 1); m'(2n + 1) = m'(2n).f(m(2n), 2n).f(m(2n), 2n).mir(m'(2n)); 
               m(2n) = m(2n - 1).f(m'(2n - 1), 2n - 1).f(m'(2n - 1), 2n - 1).mir(m(2n 
               - 1)); m'(2n) = m'(2n - 1).m(2n - 1).f(m(2n - 1), 2n - 1).c(m'(2n 
               - 1), 2n); where f(m, n) is the alphabetic morphism i := i + 2^n 
               [example: f(0 0 1 1 2 3 3 2 2 3 3 2 1 1 0 0, 2) = 4 4 5 5 6 7 7 6 
               6 7 7 6 5 5 4 4]; c(m, n) is the complementation to 2^n - 1 alphabetic 
               morphism [example: c(0 0 1 1 2 3 3 2 2 3 3 2 1 1 0 0, 3) = 7 7 6 
               6 5 4 4 5 5 4 4 5 6 6 7 7]; and mir(m) is the mirror operator [example: 
               mir(0 1 1 0 0 0 1 1 2 2 3 3 3 2 2 3) = 3 2 2 3 3 3 2 2 1 1 0 0 0 
               1 1 0].
%F A059253 a(n) = A025581(A163358(n)) = A002262(A163360(n)) = A059905(A163356(n)).
%Y A059253 See also the y-projection, m(3), A059252 as well as A163538, A163540, 
               A163542, A059261, A059285, A163547 and A163528.
%Y A059253 Sequence in context: A046918 A060287 A165001 this_sequence A108133 A014499 
               A055778
%Y A059253 Adjacent sequences: A059250 A059251 A059252 this_sequence A059254 A059255 
               A059256
%K A059253 nonn
%O A059253 0,9
%A A059253 Claude Lenormand (claude.lenormand(AT)free.fr), Jan 23 2001
%E A059253 Extended by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), 
               Aug 01 2009

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