bogus OGF in A002113 (and very many others)

[N. J. A. Sloane]

On Tue, May 13, 2008 at 2:24 PM, Peter Pein <petsie at dordos.net> wrote:
> N. J. A. Sloane schrieb:
>
>
> > Mitch,  I found the letter that Elizabeth Morgan
>  > wrote to me on April 6 1978, and i will add
>  > a more precise definition to A005045.
>  >
>  > Neil
>  >
>
>  Neil, I am afraid you made three typos. The formula reads:
>  " Let n = 3k, 3k-1 or 3k-2 according as n == 0, 2 or 1 mod 3, for n>=3.
>
>  Then a(n) = Sum_{ i=0,...,n-k } Sum_{ m=max(0,2i-n),...,floor(i/2) } Sum_{
>  r=0,...,floor(i/2)-m } c(i,m,r), where c(i,m,r) = n-2i+m+1 when m+r != i/2, or
>  = floor((m-2i+m+2)/2) when m+r = i2. "
>
>  But I get the listed values using:
>  " Let n = 3k, 3k-1 or 3k-2 according as n == 0, 2 or 1 mod 3, for n>=3.
>
>  Then a(n) = Sum_{ i=1,...,n-k } Sum_{ m=max(0,2i-n),...,floor(i/2) } Sum_{
>  r=0,...,floor(i/2)-m } c(i,m,r), where c(i,m,r) = n-2i+m+1 when m+r != i/2, or
>  = floor((n-2i+m+2)/2) when m+r = i/2. "
>
>  (i goes from *1* to n-k; c(i,m,r) has the value floor(*n*-2i+m+2)/2) if m+r ==
>  i */* 2)
>
>  Could some of the readers please check these changes?

Neil has corrected the mma.

But to his question about whether the gf matches this formula

But there's really a further question..does the gf/formula correspond
to the description, and really, -how- do they correspond (assuming
they do)? Is that in the Morgan thesis?

Mitch



Mitch said:

But there's really a further question..does the gf/formula correspond
to the description, and really, -how- do they correspond (assuming
they do)? Is that in the Morgan thesis?

about g.f.'s.  Just the complicated formula that I copied
- making those typos - into the %F lines.

Neil