I’ve come up with an idea of an integer sequence. It can be formulated (perhaps a bit loosely) as follows: **For n points N(n) is the number of configurations where each point either lies on some circle or is a center of some circle. Each point lying on a circle can belong to only 1 circle and each center point can be the center of only 1 circle.**

Then *N(1) = 2 N(2) = 5 N(3) = 10 N(4) = 20
N(5) = 36*

(I double checked N(5) but there is no guarantee that it is the right number)

Depending on how *N(0)* is defined (*N(0)=0 or N(0)=1*) this sequence very well can be **A000712**. However it appears that my description is new, so it easily can be another sequence.

MathOverflow Asked by A Z on December 29, 2020

1 AnswersYour sequence is the same as the linked OEIS sequence. This is the

Number of partitions of $n$ into parts of two kinds.

In your case, the two kinds are circles for which the centre is occupied and circles for which the centre is not occupied. See the "example" section in the OEIS entry where you can match with your worked out example.

Correct answer by Christopher Beem on December 29, 2020

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