Talk:Truncated triangular pyramid number

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symmetric truncations

The number to be removed (truncated) may be same or different from each of the vertices - but all numbers being removed would be a smaller tetrahedral number (or triangular pyramidal number) by itself.

The source cited says no such thing. If I may indulge in a bit of original research: this table shows the counts in tetrahedra with equal tetrahedra removed from each corner.

0	1	2	3	4
4	0
10	6
20	16	4
35	31	19
56	52	40	16
84	80	68	44
120	116	104	80	40
165	161	149	125	85

Some of these are indeed tetrahedral numbers, but most are not. —Tamfang (talk) 05:37, 28 October 2024 (UTC)[reply]

Unfortunately it looks like this entire article is original research based on misunderstanding the OEIS sequence. Per the OEIS description, the sequence A051937 is constructed by removing 9 balls (one 3-ball triangle from each corner) from each layer of a tetrahedral pyramid up to (and including) the layer of side-length 4 (layers of smaller length side are completely removed as they have fewer than 9 balls). The author of this article seems to have invented a completely fictional construction that seems to reproduce some of the entries in this sequence, but also a lot more integers that are not included in the OEIS sequence.

As a separate matter, this sequence seems to not be significant in math, crystallography, or any other field as far as I can tell. I think this article should be deleted. Eigenbra (talk) 18:07, 28 October 2024 (UTC)[reply]

Such is my impression as well. —Tamfang (talk) 04:49, 29 October 2024 (UTC)[reply]

I have proposed for deletion based on these concerns Eigenbra (talk) 16:42, 11 March 2025 (UTC)[reply]

@Eigenbra i would not doubt your well meaning reviews and now proposal to delete - if you could only replace this existing content which you find not useful and instead you provide / replace the existing content with a simple layman definition for "truncated triangular pyramid number" in this article - which I did not find on Wikipedia when I was searching last year and so then compiled all this information based on own efforts and readings on the net.

Regards and good day, Jn.mdel (talk) 02:30, 14 March 2025 (UTC)[reply]

@Jn.mdel There are two main issues with the article, that I simply think are not remediable. Currently, almost all of the content in the article is WP:OR. It is also just plain wrong, as I explained above. However, even if I were to correct it, I would just be replacing my original research for yours. It would still be original research. This is because there are simply no reliable sources discussing this sequence except OEIS. Per NPOSSIBLE, this is a notability issue. We simply can't have a Wikipedia article for every OEIS sequence. The sources you cited are not about the sequence this article is about, and your attempts to link them to this sequence are just more original research (WP:SYNTH). Eigenbra (talk) 13:53, 14 March 2025 (UTC)[reply]

@Eigenbra Thank you for an elaborate reply. I think I would leave it at this as you mention that - there are simply no reliable sources discussing this sequence except OEIS.

I am no mathematician - however I did still try to find something more for a simple definition and I guess that this might probably be something like a "SIMILAR SHAPE" Partition Function (Number Theory) series - which are all very big words for me but I guess that is what this is as per my limited understanding. Jn.mdel (talk) 04:43, 15 March 2025 (UTC)[reply]

Quoting myself from above, here is a simple definition: the sequence A051937 is constructed by removing 9 balls (one 3-ball triangle from each corner) from each layer of a tetrahedral pyramid up to (and including) the layer of side-length 4 (layers of smaller length side are completely removed as they have fewer than 9 balls). Eigenbra (talk) 23:55, 15 March 2025 (UTC)[reply]

@Eigenbra The current article text refers to both symmetric and asymmetric (but "similar shaped") removals / partitions / truncations. Jn.mdel (talk) 13:28, 17 March 2025 (UTC)[reply]

I now see that I misunderstood the sentence that I quoted: it does not say that a tetrahedral number remains. —Tamfang (talk) 02:47, 18 March 2025 (UTC)[reply]

Thanks for re-visiting your earlier comment and clarifying. Accordingly I am now proceeding to remove the message flag from the article masthead - hope this is fine now. Jn.mdel (talk) 10:05, 18 March 2025 (UTC)[reply]

The two references in the lede are about two different sequences of numbers. OEIS A051937 and OEIS A005906. Which one is this article supposed to be about? Eigenbra (talk) 15:14, 19 March 2025 (UTC)[reply]

@Eigenbra Hi - the article text mentions only OEIS A000292 vis-a-vis OEIS A051937 for "Truncated triangular pyramid number" - and nowhere OEIS A005906 is mentioned. Jn.mdel (talk) 06:24, 20 March 2025 (UTC)[reply]

The MathWorld reference is about OEIS A005906, so should be removed Eigenbra (talk) 14:03, 20 March 2025 (UTC)[reply]