[seqfan] Re: sequence challenge

Alois Heinz heinz at hs-heilbronn.de
Fri Nov 25 17:20:49 CET 2011


I think it is a good idea to send interesting sequences now and make
donations right after the holidays.

You found a matrix with a smaller measure that produces a sequence
not in OEIS until now.  I think it is interesting enough to be added.  And
also your other sequences are interesting.

The measure was "sum of the absolute values of matrix elements".
Other possible measures would be "number of bits needed to encode
the matrix" or "bit sum of all numbers plus 1 for each sqrt and other
function application".

Best regards, Alois

Am 24.11.2011 07:22, schrieb Ed Jeffery:
> Alois,
> I don't feel right about submitting more sequences until I can make a donation to OEIS as everyone should. I feel bad that NJAS has to ask for donations, and it is up to us users to make sure he doesn't have to do that. Unfortunately, mine will have to be made after the holidays.
> Now, about these sequences: if your measure need not be integral, then we might suppose that the matrix need not be integral, since that wasn't made clear previously. If that is the case, then I have an even smaller measure (<9), with the matrix admitting a sequence that is also not in OEIS:
> Consider the matrix M=[(1,Sqrt(2),0);(Sqrt(2),0,1),(0,1,0)]. The entries of M total 3+2*Sqrt(2)=5.828...<  9, with the sequence being
> {[M^n]_(0,0)}={1,1,3,5,13,25,59,121,273,577,1275,2733,...}, n=0,1,2,...,
> with generating function F(x)=(1-x^2)/(1-x-3*x^2+x^3).
> [ ... ]

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