What next in 0,1,6,25,96,361,1350,5041?
benoit
abcloitre at wanadoo.fr
Sun Mar 14 12:08:49 CET 2004
> So the general recurrence seems to be
> S_k: a(n) - (k-1)a(n-1) + (k-1)a(n-2) - a(n-3) = 0
> a(n) = (k-1)a(n-1) - (k-1)a(n-2) + a(n-3)
>
>
There is also the simple 2- order recurrence here :
a(n)=(k-2)*a(n-1)-a(n-2)+2
One can consider the 2 complementary families from
(a(n-1)^r-1)^s/a(n-2) recursions, which generate integer values only
when r*s is even :
the simple case is r*s=2 producing linear recurrences for 2 types of
recursion r=1 and s=2 or r=2 and s=1 :
(i) r=1 and s=2 : a(1)=1 a(2)=k a(n)=(a(n-1)-1)^2/a(n-2) which gives
the linear relation a(n)=(k-2)*a(n-1)-a(n-2)+2
(ii) r=2 and s=1 : a(1)=1 a(2)=k a(n)=(a(n-1)^2-1)/a(n-2) which gives
a(n)=k*a(n-1)-a(n-2)
For ex. (ii) is also related to many sequence in EIS :
k=3 : A001906
k=4 : A001353
k=5: A004254
k=6 : =A001109
k=7 : A004187
....
Benoit Cloitre
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: text/enriched
Size: 946 bytes
Desc: not available
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20040314/3df0e8ca/attachment-0001.bin>
More information about the SeqFan
mailing list