Error in A115866
Dan Dima
dimad72 at gmail.com
Sun Mar 4 00:08:48 CET 2007
Hi all,
I found this more than a year ago when I tried to solve the following puzzle:
http://faculty.missouristate.edu/l/lesreid/POW08_0506.html
However I found a very simple (although infinite sum) formula for the
number of paths from (0,0,...,0) to (a(1),a(2),...,a(k)) using
"nonzero" (2^k-1) steps of the form (x(1),x(2),...,x(k)) where x(i) is
in {0,1} for 1<=i<=k, k-dimensions.
I have looked carefully on the web and I found many articles related
to this issue - Multi-Dimensional Lattice Paths with Diagonal Steps
(or various kind of steps) - but none of them matches my simple
infinite sum:
f(a(1),a(2),...,a(k)) =
Sum( (C(n;a(1)) * C(n;a(2)) * ... C(n;a(k))) / 2^{n+1} , {n,
max(a(1),a(2),...,a(k)), infinity}),
Sum( (C(n;a(1)) * C(n;a(2)) * ... C(n;a(k))) / 2^{n+1} , {n, 0, infinity}),
C(n;a)=n!/a!(n-a)! & we assumed C(n;a)=0 if n<a
Please can someone correct me if I am wrong!
Nick: If you want to compute larger terms for those sequences please
avoid recursivity - a lot of redundant work will be done ;) ... just
use straightforward "for loops" instead...
Neil: what things happen at about 8 or 9 dimensions?
Best regards,
Dan
On 3/3/07, N. J. A. Sloane <njas at research.att.com> wrote:
> David, strange things happen at about 8 or 9 dimensions,
> so I suggest you go up to dim 10
>
> of course the arrays and diagonal sequence(s) should
> also be submitted!
>
> Best
>
> Neil
>
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