[seqfan] Re: Another error?

[Max Alekseyev]

On Sat, Nov 14, 2009 at 1:23 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
> Which of A005271 & A045310 is correct, if either?  R.

They both are correct (except for the wrong offset in A045310 - it
should be 1, not 0).

A045310 counts matchings (of arbitrary size) in n-cube
while
A005271 counts perfect matchings (i.e., of the maximum size 2^n / 2 = 2^(n-1)).

E.g., for n=2, we have
1 matching of size 0 (i.e., the empty matching)
4 matchings of size 1 (i.e., an edge)
2 matchings of size 2 (that are the perfect matchings).

So, A045310(2) = 1 + 4 + 2 = 7, while A005271(2) = 2.

Regards,
Max