cp's OEIS Frontend

A339456 a(n) is the Y-coordinate of the n-th point of the space filling curve H defined in Comments section; A339455 gives X-coordinates.

%I A339456 #14 Feb 07 2021 14:32:42
%S A339456 0,0,1,1,0,-1,-1,0,0,1,2,2,3,3,2,1,1,2,2,1,0,-1,-2,-2,-1,-1,-2,-3,-3,
%T A339456 -2,-2,-1,0,0,1,1,0,-1,-1,0,0,1,2,3,4,4,5,5,4,3,3,4,4,5,6,6,7,7,6,5,5,
%U A339456 6,6,5,4,3,2,2,3,3,2,1,1,2,2,3,4,4,5,5,4,3
%N A339456 a(n) is the Y-coordinate of the n-th point of the space filling curve H defined in Comments section; A339455 gives X-coordinates.
%C A339456 We consider a hexagonal lattice with X-axis and Y-axis as follows:
%C A339456            Y
%C A339456           /
%C A339456          /
%C A339456         0 ---- X
%C A339456 We define the family {H_n, n > 0} as follows:
%C A339456 - T_1 contains the origin (0, 0) and (1, 0), in that order:
%C A339456           +-->--+
%C A339456          O
%C A339456 - for any n > 0, H_{n+1} is built from 4 copies of H_n connected with 2^(n+1) unit segments as follows:
%C A339456                +->-2->-+
%C A339456                 \     /
%C A339456                  ^   v
%C A339456                   \ /
%C A339456            +->-1->-+->-4->-+
%C A339456           O       / \
%C A339456                  v   ^
%C A339456                 /     \
%C A339456                +->-3->-+
%C A339456 - H is the limit of H_n as n tends to infinity,
%C A339456 - H visits once every unit segment (u, v) where u and v are lattice points and at least one of u or v belongs to the region { (x, y) | x > 0 or x + y > 0 }.
%H A339456 Rémy Sigrist, <a href="/A339456/b339456.txt">Table of n, a(n) for n = 0..12160</a>
%H A339456 Rémy Sigrist, <a href="/A339456/a339456.gp.txt">PARI program for A339456</a>
%H A339456 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%o A339456 (PARI) See Links section.
%Y A339456 Cf. A339455.
%K A339456 sign,look
%O A339456 0,11
%A A339456 _Rémy Sigrist_, Dec 06 2020