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.