Nagato Yuki, 225 bytes, depth 4, A063524 from A000035

…………………「・………。………………… …………。」………。・………………。・………………。…… ………………。・「・………………。… ………………。」

The next answer should start with the terms:

0, 1, 0, 0

Characteristic function of n=1, separated by slashes.

I don't know who invented the Nagato Yuki programming language. But I found an interpreter. I don't know Scala and don't know what's the correct way to run the interpreter. So I just replaced the sample Hello World program with my code, and ran sbt at the root directory, run and selected NagatoApp.

The interpreter seemed to only read one character per line. So I chose the format without input.

Brainfuck translation:

+++++++[->+++++++<]>-.-.++.-[-.+.]