A103772 (was Re: %F A128862 (?))

Ralf Stephan ralf at ark.in-berlin.de
Sun May 20 09:44:04 CEST 2007

> %Y A128862 Equals (3*A001570(n) + 1)/4.

Oh, and Zak, your sequence

%Y A103772 Equals (4*A001570(n+1) - 1)/3, n>0.


Cino,   Please remember that the convention in the OEIS
is that, if the sequence is describing a LIST
of numbers with some property, we call the number n.

As in:

Numbers n such that ....

(and the convention is that lists
begin with index 1, so lists get offset 1)

(On the other hand, if the sequence is defined recursively,
the running index is denoted by n, and usually starts with offset 0)

Concerning A129783, please remember that the OEIS is a reference
work in mathematics.  Entries in are supposed to be correct.

If you don't have a proof that an entry is correct, you
must say:

"All the entries are conjectural"


"The entries from 11 onwards are only conjectures."

For A129783, which entries are known to be correct?

Neil Sloane

Peter,  Thanks very much for this comment :

%I A122576
%S A122576 -1,3,-12,20,-45,63,-112
%F A122576 The o.g.f. appears to be x(1-2x+6x^2-2x^3+x^4)/((x-1)^3(x+1)^4) which wo
uld give a(n)=n*(n+1)*(-1+((-1)^n)*(2n+1))/8 or alternatively a(n)=((-1)^n)*b(n)*b(
n+1) where b(2n)=n^2 and b(2n+1)=2n+1.
%O A122576 1
%K A122576 ,sign,
%A A122576 Peter Bala (pbala at toucansurf.com), Apr 26 2007

Sorry for the delay. Things have been chaotic.

I am going to use your g.f. as the new definition.
I won't mention you by name, but will take the responsibilty
for this chnage myself.  (I don't want to go into details
in this email!)

Best regards


Let {a(k)} be the sequence of positive rationals where a(n) = product{k=1 
to n} k^mu(n+1-k), where mu(k) is the Mobius (Moebius) function.

(a(n) = A130088(n)/A130089(n).)

Just wondering... What is the smallest value of n where a(n) = a(m) for 

The sequence of rationals tends downwards, it seems, but it is a bumpy 
plot -- so there seems to be plenty of opportunity for the same rational 
to occur two or more times in the sequence.

Leroy Quet

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