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## Example 3

Consider , which is a Pisot number because the other root of is inside the unit circle. Then is asymptotically an integer, and indeed =

The sequence as such is not in the book (we must divide by 2) but even without division by 2, `sequences` returns:

```Matches (at most 7) found for  2 6 14 34 82 198  :

%I A2203 M0360 N0136
%S A2203 2,2,6,14,34,82,198,478,1154,2786,6726,16238,39202,94642,228486,
%T A2203 551614,1331714,3215042,7761798,18738638,45239074,109216786,
263672646
%N A2203 Companion Pell numbers: \$a(n) = 2a(n-1) + a(n-2)\$.
%R A2203 AJM 1 187 1878. FQ 4 373 66. BPNR 43.
%O A2203 0,1
%C A2203 njas
%K A2203

References (if any):

[AJM] = { American Journal of Mathematics}.
[BPNR] = P. Ribenboim, { The Book of Prime Number Records}, Springer-
Verlag, NY, 2nd ed., 1989.
[FQ] = { The Fibonacci Quarterly}.```
Instead of mentioning Pisot numbers, the sequence is (correctly) identified as being related to Companion Pell numbers. This connexion also would have been unlikely without this compendium.

jon.borwein@gmail.com