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A059253
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Hilbert's Hamiltonian walk on N X N projected onto y axis: m'(3).
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12
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| This is the Y-coordinate of the n-th term in the type I Hilbert's Hamiltonian walk A163359 and the X-coordinate of its transpose A163357.
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..65535
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FORMULA
| 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) = A025581(A163358(n)) = A002262(A163360(n)) = A059905(A163356(n)).
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CROSSREFS
| See also the y-projection, m(3), A059252 as well as A163538, A163540, A163542, A059261, A059285, A163547 and A163528.
Sequence in context: A046918 A060287 A165001 * A108133 A194883 A175453
Adjacent sequences: A059250 A059251 A059252 * A059254 A059255 A059256
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KEYWORD
| nonn
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AUTHOR
| Claude Lenormand (claude.lenormand(AT)free.fr), Jan 23 2001
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EXTENSIONS
| Extended by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Aug 01 2009
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