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# Works Citing OEIS

In order to demonstrate some of the ways in which people have found the **OEIS** useful, we have assembled a list of papers and books that reference it. The list has been broken into subsections according to the first few letters of the first author's last name.

The main reason for doing this is to update the OEIS entries with information about recent work on the sequences. People often reference sequences in the OEIS, but what they don't do is add a reference (or link) to the OEIS entry, saying something like J. Smith, Title of paper, Journal (or URL) (mentions this sequence in Section 4).

Another reason for assembling this list is to answer the question "What use is the OEIS?". By referring people to this list we can say that over 6000 people have found it helpful, and that many of these works say things like "This discovery was made with the help of the OEIS".

## Contents

## Adding more references

- Additions to these pages are welcomed.
- If you see an article, book or web page that cites the
**OEIS**, please add it to the appropriate page here. - But if you add anything to these pages, please be very careful — remember that this is a scientific database. Spell authors' names, titles of papers, journal names, volume and page numbers, etc., carefully, and preserve the alphabetical ordering.
- Follow the format of the existing entries.
- If you are unclear about what to do, contact one of the Editors-in-Chief before proceeding.
- Works are arranged in alphabetical order by author's last name.
- Works with the same set of authors are arranged by date, starting with the oldest.

## Want to help?

- If you would like to help, look for references to the
**OEIS**that are not already listed in these pages. The following are good places to look:- The arXiv
- Math Sci Net (needs a subscription)
- MATH Zentralblatt, in particular the OEIS tags
- Google and its Ngrams lab.
- Google Scholar (initialized query)
- The Journal of Integer Sequences. This journal has many papers that could be added here. It has been checked up through (roughly) article #16.1.1, Vol. 19, 2016. Any later papers that reference the
**OEIS**could be added here (and there will be a lot). If you do, please update this comment. - Journals such as the following (some require a subscription, but many university libraries subscribe). These are the journals I check first when I have a chance to visit a university library.
- American Mathematical Monthly
- Bulletin of ICA (Bulletin of the Institute of. Combinatorics and its Applications)
- Canadian Mathematical Bulletin
- Discrete Mathematics
- The Electronic Journal of Combinatorics
- The European Journal of Combinatorics
- Fibonacci Quarterly
- INTEGERS
- Journal of Combinatorial Theory (Parts A and B)
- Journal of Number Theory
- Квант (Qvant)
- The Ramanujan Journal
- SIAM J. Discrete Mathematics
- etc.

- Check the Current Periodicals shelves of your local university library!

## Adding references or links from the OEIS to these articles

- Very often, an article that references the OEIS will say something like: "this is sequence A123456 in the OEIS". When you see this, please add a reference or link from A123456 to the article. This is, after all, one of the main purposes of the OEIS, to give pointers from a sequence to the scientific literature.
- Of course we are not adding every reference to every sequence - that would be really stupid. If a sequence occurs in literature often (example: A000010), only the papers that say something new about that sequence or specifically devoted to that sequence should be referenced; otherwise, the list of references would quickly grow to infinity.

## Referencing the OEIS

If you have found the **OEIS** useful in your own work, and wish to reference it, the usual citation is

- OEIS Foundation Inc. (2018), The On-Line Encyclopedia of Integer Sequences, http://oeis.org.

To reference a particular sequence, the usual citation is

- OEIS Foundation Inc. (2018), The On-Line Encyclopedia of Integer Sequences, http://oeis.org/A123456.

The URL for the present page is http://oeis.org/wiki/Works_Citing_OEIS.

## About this page

- The list was maintained by N. J. A. Sloane until Dec 25 2010, when he partitioned it into 26 parts, converted them to MediaWiki format and moved them to the
**OEIS Wiki**. At that time it contained 1700 references.

- Since then, the length of this list has grown as follows:

## How to Process Citations Received from Google

by Neil Sloane, July 2017, with additional comments from Eric M. Schmidt.

- Every few days Google sends me a list of articles, books, web sites, etc., that have recently mentioned the OEIS. If you want to help process these , there are three basic things that need to be done for each item:
- (0) To start, see if the article is already listed here! Someone may have already added it. If it is already listed then you don't need to do anything. But be sure the authors and the title match exactly - people often write several different articles with similar titles.
- (1) Add the article, book, web site etc to the web pages on the OEIS Wiki of Works Citing the OEIS.
- (2) For each (nontrivial) OEIS sequence mentioned in the work, add either a reference or a link in the sequence entry so that it points to the work.
- (3) If there are sequences in the article that are NOT yet in the OEIS, add them to the OEIS along with a reference to the work.

### Examples

- The following are real examples from an email Google sent me on July 14 2016 (I am running about a year behind in processing these messages, which is why I need help with them).

#### Example 1

- Here is what Google sent me:

[PS] Note on Total Positivity for a Class of Recursive Matrices L Zhao, F Yan - Journal of Integer Sequences, 2016 ... [11] A. Pinkus, Totally Positive Matrices, Cambridge University Press, 2010. [12] NJA Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org. [13] RA Sulanke, Objects counted by the central Delannoy numbers, J. Integer Seq. 6 (2003), Article 03.1.5. ...

- Clicking on the link revealed that the authors' names are Liang Zhao and Fengyao Yan. Because many people have the same last name, I always try to get at least the first name of the first author.
- I also see that the article appeared in the Journal of Integer Sequences, Vol. 19 (2016), Article 16.6.5.
- Finally, at the end of the articles I see a line that says: "Concerned with sequences A000108, A002802, A006298, A008288, and A035309." That is very convenient, I don't have to search through the article to see which sequences it mentions.
- I add the following line to the CiteZ page:

# Liang Zhao and Fengyao Yan, Note on Total Positivity for a Class of Recursive Matrices, Journal of Integer Sequences, Vol. 19 (2016), Article 16.6.5.

- That is a single line, although I had to break it in two to get it to display properly here.
- The articles are arranged alphabetically, so that line goes right after the article by Jianqiang Zhao.
- Note the pound sign (#) at the start of the line, this is so that the articles get numbered.
- I also add the same line (without the pound sign) to the REFERENCES section of four of the five sequences that it mentions, A002802, A006298, A008288, and A035309. (I don't add it to the Catalan numbers, A000108, because that entry is very long and only major new articles are being added to it now.)
- So I add the line
- Liang Zhao and Fengyao Yan, Note on Total Positivity for a Class of Recursive Matrices, Journal of Integer Sequences, Vol. 19 (2016), Article 16.6.5.

- to A002802, A006298, A008288, and A035309, again making sure it goes in the right place in the alphabetical order.
- I
*could*instead have added it to the LINKS sections of those four sequences, but I don't do that because it takes more time and I have about 700 of these articles to process, with more arriving every few days.

#### Example 2

- Here is what Google sent me:

[PDF] Two Triple binomial sum supercongruences T Amdeberhan, R Tauraso - arXiv preprint arXiv:1607.02483, 2016 Page 1. arXiv:1607.02483v1 [math.NT] 8 Jul 2016 TWO TRIPLE BINOMIAL SUM SUPERCONGRUENCES TEWODROS AMDEBERHAN AND ROBERTO TAURASO Abstract. In a recent article, Apagodu and Zeilberger discuss ...

- Clicking on the link revealed that the authors' names are Tewodros Amdeberhan and Roberto Tauraso, and the title is Two triple binomial sum supercongruences. (Note that Google incorrectly capitalized the t in triple — this is typical, it is very difficult to get the capitalization correct.).
- I don't see the OEIS mentioned in the References, but by searching for the string OEIS I discover that it is mentioned on page 11 with a reference to A174123.
- I add the following line to the CiteA page:

# Tewodros Amdeberhan and Roberto Tauraso, Two triple binomial sum supercongruences, arXiv preprint arXiv:1607.02483, 2016.

- That is a single line, although I had to break it in two to get it to display properly here.
- The articles are arranged alphabetically, so that line goes right after the article by Tewodros Amdeberhan and Richard P. Stanley.
- Note the pound sign (#) at the start of the line, this is so that the articles get numbered.
- Normally, I would also add the same line (without the pound sign) to the REFERENCES section of A174123. However, in this case I see that this article is lready mentioned there, in the LINKS section, like this:

Tewodros Amdeberhan and Roberto Tauraso, <a href="http://arxiv.org/abs/1607.02483">Two triple binomial sum supercongruences</a>, arXiv:1607.02483 [math.NT], Jul 08 2016.

- Note that I have a choice here. I could add the article to the REFERENCES section of the entry or to the LINKS section. I usually add it to the REFERENCES section, because that does not require any additional formatting.
- Likewise, when I add it to CiteA, I could add it as shown above, or I could instead have used a template format, like this:

{{arxiv|1607.02483}}

But both of these special formats take time, so normally I don't use them, because I have about 700 of these articles to process, with more arriving every few days. And having two different formats for the same article is particularly annoying.

- The main purpose of the OEIS is to provide information about a sequence you are studying, and if we can tell you it is mentioned in an article in the arXiv, you will be very happy and you won't care if we show you a reference or a link!

#### Example 3

- This one is different, because it appeared in a relatively obscure journal, so now we also give the DOI.
- Here is what Google sent me:

[PDF] On the k-Jacobsthal Lucas Numbers of Arithmetic Indexes S Uygun - International Journal of Contemporary Mathematical …, 2016 ... J. Contemp. Math. Sciences, 3 (2008), no. 13, 605-614. [9] NJA Sloane, The On-Line Encyclopedia of Integer Sequences, 2006. [10] K. Uslu, S. Uygun, The (s,t) Jacobsthal and (s,t) Jacobsthal-Lucas Matrix sequences, ARS Combinatoria, 108 (2013), 13-22. ...

- After clicking on the link, I can create a detailed reference:

S. Uygun, On the k-Jacobsthal Lucas Numbers of Arithmetic Indexes, International Journal of Contemporary Mathematical Sciences, Vol. 11, 2016, no. 4, 173 - 183; http://dx.doi.org/10.12988/ijcms.2016.51263.

which I will add to CiteU.

- There is also a template for DOI links, but again I never use it for lack of time.
- The bibliography lists [9] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, 2006 (note the strange date!), but there is no mention of any particular sequence, so this will not added to any OEIS entry.

### Remarks

- If you don't see a reference to the OEIS, try looking for Sloane. (A reference might simply say "Sloane's A123456".)
- Sometimes, especially in the arXiv, if you don't find the OEIS mentioned anywhere, try looking for an earlier version of the article. The OEIS may have been dropped from the bibliography, perhaps because a journal does not allow links to web sites. But the earlier version still goes into our list of citations.
- If the link to the article that Google provided doesn't work (perhaps because the article has been moved), use Google Scholar to try to locate it elsewhere on the web.
- If the link that Google provided only takes you to a paywall, you still may be able to access the bibliography of the article without paying. Or, of course, you may be able to find a copy of the article through your university, or on the arXiv, or on the author's home page.
- If all else fails, write to the author and ask for a copy of the article, explaining that we have heard that it mentions the OEIS.
- Instead of a reference to the OEIS web site, the article might reference the 1973 Handbook of Integer Sequences, the 1995 Encyclopedia of Integer Sequences, or one of the articles I have written about the OEIS. All of these are fine - they all count as citations and go into the citation lists.
- If the article in on someone's home page, or blog, or a web site like ResearchGate, give the URL where it can be found.
- Occasionally Google will send a link to an article that mentions the wrong OEIS, such as an Oceanographic Environmental Impact Statement. Naturally we do not add that to our citation lists!
- Always check that Google correctly listed all the authors.
- A recent article by Alex Kreinen, Risk Analytics, IBM, was listed with two authors, Alex Kreinen and Risk Analytics! This was a mistake, obviously Risk Analytics is simply the author's affiliation, not a coauthor!
- If there are more than four or five authors, Google tends to only list the first four.

- If there are two articles with identical sets of authors, list the oldest one first.
- Authors with "de", "De", "van", "Van" etc. in their names get listed under d, v, ...
- Authors with middle names are sometimes tricky. Of course Mary Jane Smith goes in CiteS. But many Latin American authors have a compound last name. Bernardo Recaman Santos is listed in CiteR not CiteS. Sometimes checking the bibliography, or the author's postal address, will help to identify the author's last name.
- For more about putting authors' names in the correct order, see the next section.
- If the only mention of the OEIS in the paper says" This sequence is not in the OEIS", that still counts as a citation — but be sure to add the sequence to the OEIS!
- If you would like to set up your own alert so that you can help with this project, here is what my Google Alert says: [ OEIS OR "Encyclopedia of Integer Sequences" -omphalocele ]
- There is no point in adding references or links to the very basic sequences like the all-ones sequence (A000012), the natural numbers (A000027), the squares, the triangular numbers, etc., otherwise these would have millions of references.
- It can be tricky searching PDFs for the places in an article where the OEIS citations occur. If the OEIS is listed as (say) reference 5, try searching for "[5]", "[5", or "5]" to find them. Even then, sometimes things that should be found aren't. Searching for just "5" is also possible, but often yields lots of false positives.
- If the article has a DOI, the doi template can be used to produce a URL. If there isn't one, it is preferred to link to an HTML landing page for the article (rather than a PDF), if one exists. For instance, given an article from the Journal of Integer Sequences, this page can be found by replacing ".pdf" with ".html" in the URL.

### Locating articles

- Usually the email from Google has a link that will produce the article that references the OEIS. This is needed so that we can check that it really does mention the OEIS (and not a medical condition with the same abbreviation), and to see which sequences it mentions so that we can add a reference to the article from those sequences.
- However, sometimes the article is behind a paywall, or the link no longer works. In that case there are several things you can try:
- Google Scholar is by far the most useful web site to try - it will often find a preprint or other free version of the article.
- Or you can write to the author and ask for a copy, saying that you heard that it mentioned the OEIS.
- Or you can check our "Works Citing the OEIS" pages - these are actually a very valuable source for getting information about hard-to-locate articles. And if the article is already listed then you don't need to pursue it further.
- If you know the DOI number for the article, that may help locate it.
- University libraries often have access to articles behind paywalls. And many of the OEIS editors have access to these libraries - you can always ask for help.

## Putting Authors in the Correct Order

- Citations are arranged in alphabetical order by last name. However, this is trickier than you might think!

- If there are two articles with identical sets of authors, list the oldest one first. (John Smith, 1994 goes before John Smith, 1996)

- Articles with a single author (Henry P. Smith) come before articles by that author and someone else (Henry P. Smith and John Doe)

- We don't change the order of the authors' names. If the paper is by John Zeeman and William Archer, it goes under Z not A.

- Always try to include at least the first name of the first author. Otherwise it gets hard to distinguish between people with the same last name.

- Authors with "de", "De", "van", "Van" etc. in their names get listed under d, v, ...

- Authors with middle names are sometimes tricky. Of course Mary Jane Smith goes in CiteS. But many Latin American authors have a compound last name. Bernardo Recaman Santos is listed in CiteR not CiteS. Sometimes checking the bibliography, or the author's postal address, will help to identify the author's last name.

- Once you have decided where the last name starts, sort the last names
**taking spaces and most punctuation into account**.

- When in doubt, a useful guide is to do what the unix sort command would do.

- However, we generally ignore accents. We treat é as if it were a plain e. (This is because many of us don't have keyboards that can type accents.)

- We also silently correct errors and omissions when doing the sorting. If Jean St Denis accidentally writes Jean St. Denis, we ignore the period. If a coauthor of John Horton Conway gives his name as J. Conway (and we are certain it is him) we sort it as if it were written correctly, although we don't correct the error.

- As a test, I made up some "O" names, and ran them through the sort command. Here is the result:
- O Hara
- O' Grady
- O' Hara
- O'Brian
- O'Hara
- O-Hara
- O_Hara
- Oblomov
- Oman