Q: Catalan's A000108 modulo 4 are A073267?
Max Alekseyev
maxale at gmail.com
Tue Feb 26 13:45:27 CET 2008
On Mon, Feb 25, 2008 at 2:09 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
>
> If we read the Catalan numbers A000108 modulo 4, we apparently get
> A000108(n) = A073267(n+1) mod 4 , n>=1
> which seems to be the content of Theorem 2.3 of
> Eu-Liu-Yeh's
> <a href="http://www.math.sinica.edu.tw/mathuser/file_upload/mayeh/MotzkinMod_f.pdf">Catalan and Motzkin numbers modulo 4 and 8</a> .
>
> Could s.o. with a higher mathematical background confirm this and perhaps
> submit this as a comment to A073267 ?
Richard,
I confirm that.
Actually, A073267 can be simply described as:
A073267(2^n) = 1 for n>=1;
A073267(2^n+2^m) = 2 for n>m>=1.
A073267(k) = 0 otherwise.
This is perfectly consistent with Theorem 2.3 from the aforementioned paper.
So, please submit your comment (along with the reference).
Regards,
Max
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