This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334188 #30 Feb 25 2021 21:24:36
%S A334188 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,
%T A334188 -10,-18,-14,11,17,19,-27,-25,-19,-17,-15,40,12,16,20,-28,-24,-20,-16,
%U A334188 -48,41,39,13,15,21,-29,-23,-21,-47,-49,42,34,38,14,22,-34,-30
%N 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.
%C A334188 We start with a unit square U_0 oriented counterclockwise, the origin being at the left bottom corner:
%C A334188 +---<---+
%C A334188 | |
%C A334188 v ^
%C A334188 | |
%C A334188 O--->---+
%C A334188 The configuration U_{k+1} is obtained by connecting four copies of the configuration U_k as follows:
%C A334188 | | | |
%C A334188 . + + . . + + .
%C A334188 U_k ^ v U_k ^ v
%C A334188 . + + . . + + .
%C A334188 | | | |
%C A334188 -+->-+---+ +---+->-+- -+->-+ + + +->-+-
%C A334188 --> v | | ^
%C A334188 -+-<-+---+ +---+-<-+- -+-<-+ +-<-+ +-<-+-
%C A334188 | |
%C A334188 . + + . . +->-+ .
%C A334188 U_k ^ v U_k ^ v
%C A334188 . + + . . + + .
%C A334188 | | | |
%C A334188 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).
%C A334188 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.
%C A334188 U visits once every lattice points with nonnegative coordinates and has a single connected component.
%H A334188 Rémy Sigrist, <a href="/A334188/b334188.txt">Table of n, a(n) for n = 0..5049</a>
%H A334188 Rémy Sigrist, <a href="/A334188/a334188.png">Representation of U_k for k = 0..5</a>
%H A334188 Rémy Sigrist, <a href="/A334188/a334188_1.png">Colored representation of U_7</a>
%H A334188 Rémy Sigrist, <a href="/A334188/a334188_2.png">Colored representation of the table for 0 <= x, y, <= 1023</a> (where the hue is function of T(y, x))
%H A334188 Rémy Sigrist, <a href="/A334188/a334188.gp.txt">PARI program for A334188</a>
%e A334188 Square array starts:
%e A334188 n\k| 0 1 2 3 4 5 6 7
%e A334188 ---+----------------------------------------
%e A334188 0| 0....1....2....3 8....9...10...11
%e A334188 | | | | |
%e A334188 1| -1 -6...-7 4 7 18...17 12
%e A334188 | | | | | | | | |
%e A334188 2| -2 -5 -8 5....6 19 16 13
%e A334188 | | | | | | |
%e A334188 3| -3...-4 -9 -26..-27 20 15...14
%e A334188 | | | | |
%e A334188 4| -12..-11..-10 -25 -28 21...22...23
%e A334188 | | | | |
%e A334188 5| -13 -18..-19 -24 -29 -34..-35 24
%e A334188 | | | | | | | | |
%e A334188 6| -14 -17 -20 -23 -30 -33 -36 25..
%e A334188 | | | | | | | |
%e A334188 7| -15..-16 -21..-22 -31..-32 -37 -102..
%e A334188 | | |
%o A334188 (PARI) See Links section.
%Y A334188 See A163334, A323335 and A334232 for similar sequences.
%Y A334188 See A334220, A334221, A334222 and A334223 for the coordinates of the curve.
%K A334188 sign,look,tabl
%O A334188 0,4
%A A334188 _Rémy Sigrist_, Apr 18 2020