Hypercomplex numbers and combinatorial sums. (II)

["Marko Riedel" <mriedel@xxxxxxxxxxxxx>]

Hello there,

I forgot: we are trying to sum

   m[r] = Sum(C(n m + (n-1), n k + r), k, 0, m)

by using a linear system of equations.

The first equation is

    m[0] + m[1] + ... + m[n-1] = 2^(n * m + (n-1))

Choose w hypercomplex such that (this is the interesting part)

    w^n = 1

where n is prime.

The remaining equations are obtained from 

    [(1+w)^n]^m (1+w)^(n-1) =
    m[0] + m[1] w + m[2] w^2 + ... + m[n-1] w^(n-1)

There are (n-1)/2 of these, every one of them with a different power
of w.

Best regards,

-- 
+------------------------------------------------------------+
| Marko Riedel, EDV Neue Arbeit gGmbH, mriedel@neuearbeit.de |
| http://www.geocities.com/markoriedelde/index.html          |
+------------------------------------------------------------+