[seqfan] Re: A123712 and A178212
Peter Luschny
peter.luschny at googlemail.com
Fri Feb 10 18:34:55 CET 2012
In response to Mats Granvik's message
http://list.seqfan.eu/pipermail/seqfan/2012-February/016393.html
Let me see if I understand this. You replace the dependency
of A123706 from A010766, as for example expressed with Sage,
def A123706_triangle(dim) :
m = matrix(QQ, dim, dim, lambda n, k: (n+1)//(k+1))
return m.inverse()
by applying a recursion (according to Wikipedia invented by
you (see also [1] and [2])). Further you indicate that applying
the same recursion to different initial values will also lead
to other highly significant arithmetical functions.
This looks all very interesting to me. However, I am not sure
if everyone on this list likes the computational turn this
might get and therefore I opened a new thread on seqcomp [3]
for those who are interested to follow.
Peter
[1] http://math.stackexchange.com/questions/48946/do-these-series-converge-to-the-mangoldt-function
[2] http://math.stackexchange.com/questions/84177/is-this-sum-equal-to-the-mobius-function
[3] http://groups.google.com/group/seqcomp
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