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 A334232 T(n, k) is the number of steps from the point (0, 0) to the point (k, n) along the H-order curve; a negative value corresponds to moving backwards; square array T(n, k), n, k >= 0 read by antidiagonals downwards. 6
 0, 1, -1, 4, 2, -2, 5, 3, -5, -3, 12, 6, -6, -4, -12, 13, 11, 7, -7, -11, -13, 16, 14, 10, 8, -8, -10, -14, 17, 15, 23, 9, -23, -9, -17, -15, 48, 18, 22, 24, -24, -22, -18, -16, -48, 49, 47, 19, 21, 25, -25, -21, -19, -47, -49, 52, 50, 46, 20, 28, 26, -26, -20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The H-order curve is built as follows: - we start we a unit square H_0 oriented counterclockwise, the origin being at the left bottom corner:          +---<---+          |       |          v       ^          |       |          O--->---+ - the configuration H_{k+1} is obtained by connecting four copies of the configuration H_k as follows:              |   |                               |   |          .   +   +   .                       .   +   +   .      H_k     ^   v     H_k                       ^   v          .   +   +   .                       .   +   +   .              |   |                               |   |     -+->-+---+   +---+->-+-             -+->-+   +-<-+   +->-+-                                 -->          v           ^     -+-<-+---+   +---+-<-+-             -+-<-+   +->-+   +-<-+-              |   |                               |   |          .   +   +   .                       .   +   +   .      H_k     ^   v     H_k                       ^   v          .   +   +   .                       .   +   +   .              |   |                               |   | - the H-order curve corresponds to the limit of H_k as k tends to infinity, - the H-order curve visits once every lattice points with nonnegative coordinates and has a single connected component. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..5049 GeoWave Developper Guide, Spatial Index Rémy Sigrist, Representation of H_k for k = 0..5 Rémy Sigrist, PARI program for A334232 EXAMPLE Square array starts:   n\k|    0    1    2    3    4    5    6    7   ---+----------------------------------------     0|    0....1    4....5   12...13   16...17      |    |    |    |    |    |    |    |    |     1|   -1    2....3    6   11   14...15   18      |    |              |    |              |     2|   -2   -5...-6    7   10   23...22   19      |    |    |    |    |    |    |    |    |     3|   -3...-4   -7    8....9   24   21...20      |              |              |     4|  -12..-11   -8  -23..-24   25   28...29      |    |    |    |    |    |    |    |    |     5|  -13  -10...-9  -22  -25   26...27   30      |    |              |    |              |     6|  -14  -17..-18  -21  -26  -29..-30   31      |    |    |    |    |    |    |    |    |     7|  -15..-16  -19..-20  -27..-28  -31   32 PROG (PARI) See Links section. CROSSREFS See A334188 for a similar sequence. See A334233, A334234, A334235 and A334236 for the coordinates of the curve. Sequence in context: A245518 A217462 A016510 * A244681 A023634 A199609 Adjacent sequences:  A334229 A334230 A334231 * A334233 A334234 A334235 KEYWORD sign AUTHOR Rémy Sigrist, Apr 19 2020 STATUS approved

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Last modified April 11 09:54 EDT 2021. Contains 342886 sequences. (Running on oeis4.)