Here is an animation (thanks to Ian Rust) showing how the even values of n approach the GCD pattern (OEIS A054521) as the values increase https://streamable.com

Here is an animation (thanks to Ian Rust) showing how the even values of n approach the GCD pattern (OEIS A054521) as the values increase https://streamable.com/l7r96 https://streamable.com/l7r96 however the odd values of n are not equivalent to the GCD pattern.