Two messages

[Michael Somos]

Robert G. Wilson wrote :

>  The second sequence is A(-2) = A(-1) =1, A(n) = 3*A(n-1) + 2^n. 
> I am not entirely happy with this 'definition.'

It is not so bad, but only one of many. How about the generating function ?

gp> for(n=0,13,print1(polcoeff((1-x)/((1-2*x)*(1-3*x)),n)","))
1,4,14,46,146,454,1394,4246,12866,38854,117074,352246,1058786,3180454,

Antreas P. Hatzipolakis wrote :

> and is the sequence  A027649 in _EIS_

As a quick lookup shows, and now we can add the "G.f.:" for it. Also, it
has an order two recursion as a consequence. Shalom, Michael

-- 
Michael Somos <somos at grail.cba.csuohio.edu>     Cleveland State University
http://grail.cba.csuohio.edu/~somos/            Cleveland, Ohio, USA 44115