# [seqfan] Re: Walk like an Egyptian

Maximilian Hasler maximilian.hasler at gmail.com
Fri Feb 20 21:31:39 CET 2009

```c(n,k,m=1)={ n==1 & return(numerator(k)==1 & denominator(k)>=m);
sum( i=max(m,1\k+1),n\k, c(n-1, k-1/i, i))}

for(n=1,6, for(k=1,n, print1( c(n,k)"\t"));print)
1
1       1
3       1       1
14      4       1       1
147     17      4       1       1
3462    164     18      4       1       1
294314  3627    167     18      4       1       1

i.e.
c(7,1)=A002966(7)=294314
and c(7,2..7) = 3627    167     18      4       1       1

So the next terms in A156869 are:
294314, 3627, 167, 18, 4, 1, 1,
159330691, 297976, 3644, 168, 18, 4, 1, 1

(my very basic code takes over 2.5 min to calculate c(n,n-6)...)

The next term in A156870 is 298165.
(= c(n,n-6) for n=12,13,14,...,20,...)

Maximilian

c(8,2)
%31 = 297976

c(9,3)
%7 = 298144

c(10,4)
%37 = 298161

c(11,5)
%32=298164

c(12,6)
%33 = 298165
***   last result computed in 2mn, 45,609 ms.

c(13,7)
%34 = 298165
***   last result computed in 2mn, 46,484 ms.

c(20,14)
%36 = 298165
***   last result computed in 2mn, 44,219 ms.

On Fri, Feb 20, 2009 at 3:00 PM, Jens Voß <jens at voss-ahrensburg.de> wrote:
> (submitted to the OEIS as A156869; the sum over all k is A156871)
...
> I stated this observation as a conjecture in A156869, however I have
> only very little empirical evidence of this hypothesis, much less a
> proof to it. (The sequence 1, 4, 18, 168, 3648, ... in the column are
> submitted as A156870.)
>
> Are there any egyptologists on this mailing list that can either come up
> with additional terms to the sequences A156869 - A156871 or prove the
> conjecture?

```