A390425 Number of distinct lattice points on the Lévy C curve after n iterations.

2, 3, 5, 9, 16, 30, 57, 111, 214, 416, 809, 1579, 3073, 5995, 11697, 22853, 44650, 87342, 170937, 334839, 656199, 1286913, 2525057, 4957333, 9736760, 19133868, 37616337, 73986039, 145578997, 286570159, 564326161, 1111725765, 2190893486, 4319165522, 8517736521

Offset

0,1

Comments

The points in C curve iteration level n are coordinate pairs {A332251(t),A332252(t)} for 0 <= t <= 2^n.

Some lattice points are visited multiple times (up to 4 times) and a(n) is the number of distinct points visited.

Links

Kevin Ryde, Table of n, a(n) for n = 0..700

Kevin Ryde, Iterations of the Lévy C Curve, see index "V visited points" with a(k) = V_k.

Kevin Ryde, PARI/GP code and generating function

Wikipedia, Lévy C curve

Index entries for linear recurrences with constant coefficients, signature (11, -54, 159, -316, 423, -244, -535, 2042, -3959, 5480, -5369, 2460, 3377, -10988, 18291, -22617, 22272, -17938, 11174, -3128, -4892, 12848, -22600, 34136, -45648, 57424, -67424, 70496, -67072, 58176, -40448, 18304, 0, -12544, 15872, -9216, 2048).

Example

For n=4 the curve is points t=0 to t=16 as follows and there are a(4) = 16 distinct points since t=7 and t=9 are the same location.
       11---10---9,7---6----5
        |         |         |
  13---12         8         4----3
   |                             |
  14                             2
   |                             |
  15---16                   0----1

Prog

(PARI) \\ See links.

Crossrefs

Cf. A332251, A332252.

Sequence in context: A072176 A329700 A217282 * A047061 A136169 A047041

Adjacent sequences: A390422 A390423 A390424 * A390426 A390427 A390428

Keyword

nonn

Author

Jacob Lim, Nov 05 2025

Extensions

a(15) onward from Kevin Ryde, Dec 13 2025

Status

approved