Newbie Question & Contributions - a(17)-a(18) of A129551 and A129552

[Jonathan Carroll]

Hello, My first edits, a(17)-a(18) of A129551 and A129552, were approved this week, and I'd like to thank Alois Heinz and Andrew Howroyd for the quick review. I plan to keep contributing at whatever pace the editors find useful. I'm Jonathan Carroll, Long Island, New York. I'm not a mathematician; I work in insurance and I solve puzzles of all kinds for fun. I recently started looking at math problems and found your OEIS site, which is so cool and I'm surprised I hadn't found it sooner. The use of Claude and AI has allowed me to look at more complicated problems than I would generally work on, so I am not hiding anything, pretty much anything I bring to the table will include the use of AI.

I wrote a program that finds relations between OEIS entries that neither entry records: one sequence as a shift, sum, difference, subsequence, convolution, transform, or small integer combination of others, checked with exact arithmetic on every published term, and reported only when the entries don't already cross-reference each other.

On the "more"/"hard" entries it re-found about 6,300 relations already recorded and about 700 that aren't. Two I think are worth an editor's eye, not yet submitted:

A006766(n) = A038119(n) - A000105(n) (strictly 3-D polycubes = all free polycubes minus planar ones), giving a(13)-a(22).

A079572(n) = A024607(n) + A004250(n) (connected paw-free graphs, Olariu 1988), giving a(15)-a(17).

"Holds on every published term" isn't proof; the same search finds A162165 = A162389, which fails at n = 37. I'd only submit relations with a reason they're true.

Would you want all of these submissions? I don't want to load you up with submissions if they're fluff. How would the editors like this used? (a) I publish the program and its candidate list for anyone to pick from; (b) a few edits a week through the normal process, proofs first; (c) something that's worked before. It also flags eight recorded formulas that seem to fail on a published term of their own entry; happy to send that list privately.

Thank you, its not my intent to submit volume data that's not useful to anyone.

Jonathan Carroll

[Antti Karttunen]

On Sat, Sep 26, 2026 at 6:38 AM Jonathan Carroll <carro...@gmail.com> wrote:

Hello, My first edits, a(17)-a(18) of A129551 and A129552, were approved this week, and I'd like to thank Alois Heinz and Andrew Howroyd for the quick review. I plan to keep contributing at whatever pace the editors find useful. I'm Jonathan Carroll, Long Island, New York. I'm not a mathematician; I work in insurance and I solve puzzles of all kinds for fun. I recently started looking at math problems and found your OEIS site, which is so cool and I'm surprised I hadn't found it sooner. The use of Claude and AI has allowed me to look at more complicated problems than I would generally work on, so I am not hiding anything, pretty much anything I bring to the table will include the use of AI.

I wrote a program that finds relations between OEIS entries that neither entry records: one sequence as a shift, sum, difference, subsequence, convolution, transform, or small integer combination of others, checked with exact arithmetic on every published term, and reported only when the entries don't already cross-reference each other.

On the "more"/"hard" entries it re-found about 6,300 relations already recorded and about 700 that aren't. Two I think are worth an editor's eye, not yet submitted:

A006766(n) = A038119(n) - A000105(n) (strictly 3-D polycubes = all free polycubes minus planar ones), giving a(13)-a(22).

A079572(n) = A024607(n) + A004250(n) (connected paw-free graphs, Olariu 1988), giving a(15)-a(17).

Please see also entries:

https://sequencedb.net/s/A006766

https://sequencedb.net/s/A079572

in Jon Maiga's database, where he has automatically searched for gazillions of such apparent relations. Beware that the indexing often has ±1 mismatch there for technical/legacy reasons, so the exact offsets have to be checked manually.

When the apparent relation holds up to some large n (and it's not wholly tautologous), or if there is an apparent connection between at least the two of the three sequences, I think such conjectured formulas could be worthwhile to be "lifted up" to the OEIS itself, with a note like "apparently" added, to potentially catch the attention of another person (or AI) that might then try to prove it.

Best regards,

Antti

"Holds on every published term" isn't proof; the same search finds A162165 = A162389, which fails at n = 37. I'd only submit relations with a reason they're true.

Would you want all of these submissions? I don't want to load you up with submissions if they're fluff. How would the editors like this used? (a) I publish the program and its candidate list for anyone to pick from; (b) a few edits a week through the normal process, proofs first; (c) something that's worked before. It also flags eight recorded formulas that seem to fail on a published term of their own entry; happy to send that list privately.

Thank you, its not my intent to submit volume data that's not useful to anyone.

Jonathan Carroll

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[John Mason]

Jonathan

IMHO,  A006766(n) = A038119(n) - A000105(n)   is certainly worth including. While you're at it, an extra comment "This sequence enumerates strictly 3D polycubes." would be a good idea, since the Name field lacks the word "strictly".

john

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