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A059252
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Hilbert's Hamiltonian walk on N X N projected onto x axis: m(3).
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12
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0, 0, 1, 1, 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, 5, 5, 6, 6, 7, 7, 7, 6, 6, 7, 7, 7, 6, 6, 5, 4, 4, 5, 5, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 8, 8, 8, 9, 9, 10, 10, 11, 11, 11, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 14, 14, 15, 15, 14
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OFFSET
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0,5
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COMMENTS
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This is the X-coordinate of the n-th term in the type I Hilbert's Hamiltonian walk A163359 and the Y-coordinate of its transpose A163357.
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..65535
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FORMULA
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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].
a(n) = A002262(A163358(n)) = A025581(A163360(n)) = A059906(A163356(n)).
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EXAMPLE
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[m(1)=0 0 1 1, m'(1)= 0 1 10] [m(2) =0 0 1 1 2 3 3 2 2 3 3 2 1 1 0 0, m'(2)=0 1 1 0 0 0 1 1 2 2 3 3 3 2 2 3]
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CROSSREFS
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See also the y-projection, m'(3), A059253, as well as: A163539, A163540, A163542, A059261, A059285, A163547 and A163529.
Sequence in context: A048466 A096838 A096007 * A030620 A110764 A107901
Adjacent sequences: A059249 A059250 A059251 * A059253 A059254 A059255
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KEYWORD
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nonn
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AUTHOR
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Claude Lenormand (claude.lenormand(AT)free.fr), Jan 23 2001
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EXTENSIONS
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Extended by Antti Karttunen, Aug 01 2009
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STATUS
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approved
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