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Old 2016-09-10, 05:47   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default A034856/

Hi Math People,

I was exploring oeis.org. This is the Online Encyclopedia of integer sequences.

oeis.org/A034856/

Many people have double checked this encyclopedia.

I read that for A034856, a(n) reduces to n*(n+3)/2 - 1.

When I work it through, I reach the expression n*(n-1)/2 -1.

Probably I am wrong and the encyclopedia is right.

I assume that binomial(n,k) = n!/(k!(n-k)!).
Can someone else check this expression?

Regards,
Matt
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Old 2016-09-10, 07:25   #2
GP2
 
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Sep 2003

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Quote:
Originally Posted by MattcAnderson View Post
oeis.org/A034856/

I read that for A034856, a(n) reduces to n*(n+3)/2 - 1.

When I work it through, I reach the expression n*(n-1)/2 -1.
Code:
binomial(n+1, 2) + (n − 1)

    n*(n+1)     2*(n−1)
=   -------  +  -------
       2           2

    n*n + 1*n + 2*n − 2
=   -------------------
             2

    n*(n+3) − 2
=   -----------
         2

    n*(n+3)
=   -------  −  1
       2
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Old 2016-09-10, 14:20   #3
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Thank you GP2. You are correct.

Regards,
Matt
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