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A059261
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Hilbert's Hamiltonian walk on N X N projected onto the first diagonal: M(3) (sum of the sequences A059252 and A059253).
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6
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| The interest comes from a simplest recursion than the cross-recursion, dependent on parity, governing the projections onto the x and y axis.
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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; 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]
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CROSSREFS
| Cf. the x-projection m(3), A059252 and the y-projection m'(3), A059253. See also: A163530, A059285, A163547.
Sequence in context: A169809 A076258 A030330 * A162330 A134967 A084612
Adjacent sequences: A059258 A059259 A059260 * A059262 A059263 A059264
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KEYWORD
| nonn
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AUTHOR
| Claude Lenormand (claude.lenormand(AT)free.fr), Jan 24 2001
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EXTENSIONS
| Extended by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Aug 01 2009
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