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.

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