Before I go over the updates related to my work, I want to mention that OEIS is celebrating 400k sequences . There was a contest to choose sequence A400000 and the City-Building Sequence won the competition. Read the comments section and the example section to better understand the sequence. There is also a City-Building Sequence entry in MathWorld. Let’s not forget the runners-up.
I was actually working on a sequence to enter the A400000 competition that used Lill’s method. Unfortunately, I found out that the mechanism for my sequence generates A330714. I already have a new similar idea that seems to generate a new sequence, but I’ll leave that for another post. Right now, I want to mention some updates that resulted in new OEIS edits or new MathWorld entries.
A005568 Comment
I made a comment for sequence A005568. My comment says “Historical note: Erdős and Kaplansky (1946) considered a king starting at (0,0) on a two-dimensional chessboard formed by N^2 and stated that, when the king is restricted to horizontal and vertical moves, (C(n))^2 counts the number of 2n-step returns to the starting point. Motzkin (1948, footnote 4), citing their paper, corrected this to C(n)*C(n+1), which is this sequence.”
The comment cites “P. Erdős and I. Kaplansky, Sequences of Plus and Minus, Scripta Mathematica, Vol. 12 (1946), pp. 73-75”. You can see the article below. The other paper cited is “Th. Motzkin, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products, Bull. Amer. Math. Soc., Vol. 54 (1948), pp. 352-360. See footnote 4”.
OEIS Added Links
I have added links to 2 OEIS entries. I added a link to A396572. I have added a link to a Youtube video created by the author of the sequence, Gary Sims. His Youtube channel is “Gary Explains” and the video is called “My First OEIS Sequence: Number of Unique States for a Loop of Numbers Under XOR Operations“. Gary didn’t bother to add the Youtube link to the sequence page, so I did the edit. Gary has a lot of interesting videos explaining technology, so you should subscribe to his channel or at least watch some of his videos.
I also have added a link to sequence A058038. The sequence appears in the MathWorld entry for “Whittaker’s Root Series”, so I have added the link to the sequence. The Whittaker’s Root Series entry was created after I made a MathWorld submission in 2023 where I mentioned that Whittaker’s Root Series method should have an entry. A few weeks ago I got an email from Eric W. Weisstein that mentioned the new entry. Good to see that Whittaker’s method finally has an entry in an important math encyclopedia 🙂
More MathWorld Updates
Another pleasant surprise was the fact that my article on Frégier’s Theorem is cited in the theorem’s MathWorld entry. In 2023 I made another MathWorld suggestion where I mentioned the special case of rectangular hyperbolas and I also provided a link to my post. I am not gonna lie, it’s nice to see my name cited in an important math encyclopedia.
A more recent submission or suggestion I made to MathWorld was about mechanical methods for solving polynomial equations. On my math page I have a “Graphical and Mechanical Methods for Solving Polynomial Equations” section that has a link to a paper by Dr. R.F. Muirhead. In the Linkage entry , a section was added that talks about Muirhead’s paper and mechanism.
Final Notes
In the near future I may work on the new OEIS sequence I have alluded above. I also have to prepare a sequence described by Newton that is connected to A224446. You can already see that the sequence has a comment by me that says “The sequence appears in Newton’s De Analysi (1669) and De Methodis (1671) in connection to the literal equation y^3 + (a^2)y – 2a^3 + axy – x^3 = 0. y is expressed as an infinite series of x. a(n) appears in the denominators of the infinite series. For more details see the links to Charles Hutton’s book and Naoki Osada’s paper.” The new Newton sequence is just the numerators that appear in the mentioned infinite series. You can check the links to Hutton’s book and Osada’s paper to see the sequence. I am a bit amazed that this sequence mentioned by Newton is not already in the database.
Again, I want to encourage other people to do these types of OEIS edits or maybe make suggestions to MathWorld or other math resources. Maybe it’s not glamorous, but this is one of the ways we improve these math resources. We can also donate money and we can also make people aware of these resources.