then there are many methods. perhaps the simplest is by using the techniques of experimental math.

Generate the first couple of terms

0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66,...

if you do not recognize that sequence then take it over to the the OEIS. This is a tremendous online resource available to everyone so why "Rediscover America"

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TopNewestFirst recurrence:

\[a(n)=\frac{1}{2} \left(n^2-n\right)\]

Second recurrence:

\[a(n)=\frac{1}{2} \left(3 n-n^2\right)\]

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Hi;

If this is the recurrence

\[a(n) = 3 a(n - 1)- 3 a(n - 2) + a(n - 3)\]

then there are many methods. perhaps the simplest is by using the techniques of experimental math.

Generate the first couple of terms

0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66,...

if you do not recognize that sequence then take it over to the the OEIS. This is a tremendous online resource available to everyone so why "Rediscover America"

[a_n=\frac{1}{2} \left(n^2-n\right)/]

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Sorry, bad latexing: \[a_n=\frac{1}{2} \left(n^2-n\right)\]

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look easy but actually difficult. hehehe :)

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