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Is there a database for sequences indexed by partitions similar to Sloane's OEIS? I mean, I am aware that in the OEIS there are some arrays indexed by partitions, but I feel as though most of such sequences that frequently appear in combinatorial literature are not there.

One example of a sequence I'd really like to recognise begins as follows:

$a[1]=1$,

$a[2]=a[1^2]=2$,

$a[3]=a[1^3]=4$, $a[2,1]=8$,

$a[4]=a[1^4]=8$, $a[3,1]=a[2,1^2]=16$, $a[2^2]=24$,

$a[5]=a[1^5]=16$, $a[4,1]=a[2,1^3]=32$, $a[3,2]=a[2^2,1]=52$, $a[3,1^2]=48$.

The obvious patterns $a[\lambda]=a[\lambda^t]$ and $a[n]=2^{n-1}$, $a[n-1,1]=2^n$ do hold in general, if it helps.

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Obviously, you are very welcome to contribute your favourite statistics - send me/us a message as well if you have any questions/suggestions/remarks! –  Christian Stump Jul 4 '13 at 12:08
1  
"but I feel as though most of such sequences that frequently appear in combinatorial literature are not there" actually holds as well for our project, but we made is as simple as possible to change it! –  Christian Stump Jul 4 '13 at 12:28

2 Answers 2

up vote 3 down vote accepted

Thanks for asking this question! It really is a perfect occation for me advertising (once again) the combinatorial statistic finder http://www.FindStat.org!

To search the database for partitions, see http://www.FindStat.org/StatisticFinder/IntegerPartitions

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Thanks a lot Christian, this looks nice. Pity my statistics isn't there :-) –  Vladimir Dotsenko Jul 4 '13 at 16:59
    
You can easily go and change that, so the next person searching for it has more luck. –  Christian Stump Jul 4 '13 at 17:30

I have seen Christian Stump here on mathoverflow advertising

http://www.findstat.org/

However, your particular statistic does not appear to be in the database yet.

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1  
So such advertisements seem to make sense :-), thanks for posting! –  Christian Stump Jul 4 '13 at 12:04

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