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{{Short description|
{{Distinguish|Triangular matrix}}
[[Image:BellNumberAnimated.gif|right|thumb|The triangular array whose right-hand diagonal sequence consists of [[Bell numbers]]]]
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| issue = 2
| pages = 173–178
| year = 1976| doi = 10.1080/00150517.1976.12430575 }}.</ref>
* [[Lozanić's triangle]], used in the mathematics of chemical compounds<ref>{{citation
| title = Die Isomerie-Arten bei den Homologen der Paraffin-Reihe
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| year = 1996 | doi=10.1006/jcta.1996.0087| s2cid = 15637402
}}.</ref>
In general, a triangular array is used to store any table indexed by two [[natural numbers]] where ''j'' ≤ ''i''.
==Indexing==
Storing a triangular array in a computer requires a mapping from the two-dimensional coordinates (''i'', ''j'') to a linear [[memory address]]. If two triangular arrays of equal size are to be stored (such as in [[LU decomposition]]), they can be combined into a standard [[Array (data structure)|rectangular array]]. If there is only one array, or it must be easily appended to, the array may be stored where row ''i'' begins at the ''i''th [[triangular number]] ''T<sub>i</sub>''. Just like a rectangular array, one multiplication is required to find the start of the row, but this multiplication is of two variables (<code>i*(i+1)/2</code>), so some optimizations such as using a [[Multiplication algorithm#Usage in computers|sequence of shifts and adds]] are not available.
==See also==
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