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 A334188 T(n, k) is the number of steps from the point (0, 0) to the point (k, n) along the space filling curve U described in Comments section; a negative value corresponds to moving backwards; square array T(n, k), n, k >= 0 read by antidiagonals downwards. 6
 0, 1, -1, 2, -6, -2, 3, -7, -5, -3, 8, 4, -8, -4, -12, 9, 7, 5, -9, -11, -13, 10, 18, 6, -26, -10, -18, -14, 11, 17, 19, -27, -25, -19, -17, -15, 40, 12, 16, 20, -28, -24, -20, -16, -48, 41, 39, 13, 15, 21, -29, -23, -21, -47, -49, 42, 34, 38, 14, 22, -34, -30 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS We start we a unit square U_0 oriented counter-clockwise, the origin being at the left bottom corner:          +---<---+          |       |          v       ^          |       |          O--->---+ The configuration U_{k+1} is obtained by connecting four copies of the configuration U_k as follows:              |   |                               |   |          .   +   +   .                       .   +   +   .      U_k     ^   v     U_k                       ^   v          .   +   +   .                       .   +   +   .              |   |                               |   |     -+->-+---+   +---+->-+-             -+->-+   +   +   +->-+-                                 -->          v   |   |   ^     -+-<-+---+   +---+-<-+-             -+-<-+   +-<-+   +-<-+-              |   |          .   +   +   .                       .   +->-+   .      U_k     ^   v     U_k                       ^   v          .   +   +   .                       .   +   +   .              |   |                               |   | For any k >= 0, U_k is a closed curve with length 4^(k+1) and visiting every lattice point (x, y) with 0 <= x, y < 2^(k+1). The space filling curve U corresponds to the limit of U_k as k tends to infinity, and is a variant of H-order curve. U 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 Rémy Sigrist, Representation of U_k for k = 0..5 Rémy Sigrist, Colored representation of U_7 Rémy Sigrist, Colored representation of the table for 0 <= x, y, <= 1023 (where the hue is function of T(y, x)) Rémy Sigrist, PARI program for A334188 EXAMPLE Square array starts:   n\k|    0    1    2    3    4    5    6    7   ---+----------------------------------------     0|    0....1....2....3    8....9...10...11      |    |              |    |              |     1|   -1   -6...-7    4    7   18...17   12      |    |    |    |    |    |    |    |    |     2|   -2   -5   -8    5....6   19   16   13      |    |    |    |              |    |    |     3|   -3...-4   -9  -26..-27   20   15...14      |              |    |    |    |     4|  -12..-11..-10  -25  -28   21...22...23      |    |              |    |              |     5|  -13  -18..-19  -24  -29  -34..-35   24      |    |    |    |    |    |    |    |    |     6|  -14  -17  -20  -23  -30  -33  -36   25..      |    |    |    |    |    |    |    |     7|  -15..-16  -21..-22  -31..-32  -37 -102..      |                                  |    | PROG (PARI) See Links section. CROSSREFS See A163334, A323335 and A334232 for similar sequences. See A334220, A334221, A334222 and A334223 for the coordinates of the curve. Sequence in context: A110218 A316259 A057892 * A265993 A115009 A151944 Adjacent sequences:  A334185 A334186 A334187 * A334189 A334190 A334191 KEYWORD sign,look,tabl AUTHOR Rémy Sigrist, Apr 18 2020 STATUS approved

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Last modified October 1 16:22 EDT 2020. Contains 337443 sequences. (Running on oeis4.)