A334234 - OEIS

%I #12 Apr 27 2020 23:58:38

%S 0,0,1,1,0,0,1,2,3,3,2,1,0,0,1,1,0,0,1,2,3,3,2,2,3,4,5,5,4,4,5,6,7,7,

%T 6,5,4,4,5,5,4,3,2,2,3,3,2,1,0,0,1,1,0,0,1,2,3,3,2,1,0,0,1,1,0,0,1,2,

%U 3,3,2,2,3,4,5,5,4,4,5,6,7,7,6,6,7,7,6

%N a(n) is the Y-coordinate of the point at n steps forward from the origin along the H-order curve defined in A334232; sequence A334233 gives X-coordinates.

%H Rémy Sigrist, <a href="/A334234/b334234.txt">Table of n, a(n) for n = 0..8193</a>

%H Rémy Sigrist, <a href="/A334234/a334234.gp.txt">PARI program for A334234</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%F A334232(a(n), A334233(n)) = n.

%e The "forward" branch of H-order curve starting from the origin is as follows:

%e     7|                                      32

%e      |                                       |

%e     6|                                      31

%e      |                                       |

%e     5|                            26...27   30

%e      |                             |    |    |

%e     4|                            25   28...29

%e      |                             |

%e     3|                   8....9   24   21...20

%e      |                   |    |    |    |    |

%e     2|                   7   10   23...22   19

%e      |                   |    |              |

%e     1|         2....3    6   11   14...15   18

%e      |         |    |    |    |    |    |    |

%e     0|    0....1    4....5   12...13   16...17

%e   ---+----------------------------------------

%e   y/x|    0    1    2    3    4    5    6    7

%e - hence a(25) = a(28) = a(29) = 4.

%o (PARI) See Links section.

%Y Cf. A334232, A334233.

%K nonn

%O 0,8

%A _Rémy Sigrist_, Apr 20 2020