I came up with this idea during the trip to Japan in Dec 2016. The trip was fun. I went to many places and tested authentic japanese foods. I felt motivated and wrote a draft during my free day. In July 2017, I presented this idea at the combinatorics conference in Israel. Many of my friends, including Yi, were there. It was not until lately that Yi came to visit me in Thailand when he was on his way back to China from United States. He was interested in the closure properties of this new idea and motivated me to finish off this article.
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The article Sequences: Polynomial, C-finite, Holonomic, ...