# A further family of sequences

Alexander Povolotsky apovolot at gmail.com
Sat Jun 14 01:56:46 CEST 2008

```PURRS Demo Results
Exact solution for x(n) = 9*x(-1+n)+x(-2+n)
for the initial conditions
x(0) = 1
x(1) = 1
x(n) = 1/2*(9/2-1/2*sqrt(85))^n+
+7/170*sqrt(85)*(9/2-1/2*sqrt(85))^n-
-7/170*sqrt(85)*(9/2 +1/2*sqrt(85))^n+
+1/2*(9/2+1/2*sqrt(85))^n
for each n >= 0
========================================================
PURRS Demo Results
Exact solution for x(n) = 9*x(-1+n)+x(-2+n)
for the initial conditions
x(0) = 0
x(1) = 1
x(n) = -1/85*sqrt(85)*(9/2-1/2*sqrt(85))^n+1/85*sqrt(85)*(9/2+1/2*sqrt(85))^n
for each n >= 0

AP
===========================================================
On Fri, Jun 13, 2008 at 1:58 PM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> On Fri, Jun 13, 2008 at 1:04 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
>
>> First of all, there's the old problem of offset, which I
>> shall never succeed in learning about.  Should the sequence
>> not start  0, 1, 1, 10, ... ?
>
> IMHO, this is not a pb of offset , but of initial value.
> if the first 2 values are 0,1
> then the formula
>
> a(n) = 9 a(n-1) + a(n-2).
>
> does not produce the sequence
> 1, 1, 10, 91, 829, 7552, 68797, ...
>
> Maximilian
>

Someone misunderstood my "Summer Rules" message.

I am most definitely not on vacation.

NJAS

```

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