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URL: https://oeis.org/A390425

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A390425
Number of distinct lattice points on the Lévy C curve after n iterations.
1
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, Iterations of the Lévy C Curve, see index "V visited points" with a(k) = V_k.
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
Sequence in context: A072176 A329700 A217282 * A047061 A136169 A047041
KEYWORD
nonn
AUTHOR
Jacob Lim, Nov 05 2025
EXTENSIONS
a(15) onward from Kevin Ryde, Dec 13 2025
STATUS
approved