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Pell trisection: Pell(3*n+2), n >= 0.
2

%I #23 Sep 01 2018 21:30:29

%S 2,29,408,5741,80782,1136689,15994428,225058681,3166815962,

%T 44560482149,627013566048,8822750406821,124145519261542,

%U 1746860020068409,24580185800219268,345869461223138161,4866752642924153522,68480406462161287469,963592443113182178088,13558774610046711780701

%N Pell trisection: Pell(3*n+2), n >= 0.

%C For the general trisection of a sequence see a _Wolfdieter Lang_ comment under A187357.

%H Colin Barker, <a href="/A187362/b187362.txt">Table of n, a(n) for n = 0..850</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,1).

%F a(n) = Pell(3*n+2), n >= 0, with Pell(n):=A000129(n).

%F O.g.f.: (2+x)/(1-14*x-x^2).

%F a(n) = 14*a(n-1) + a(n-2), a(-1)=1, a(0)=2.

%F a(n) = (((7-5*sqrt(2))^n*(-3+2*sqrt(2)) + (3+2*sqrt(2))*(7+5*sqrt(2))^n)) / (2*sqrt(2)). - _Colin Barker_, Jan 25 2016

%t Table[Fibonacci[3n + 2, 2], {n, 0, 20}] (* _Vladimir Reshetnikov_, Sep 16 2016 *)

%o (PARI) Vec((2+x)/(1-14*x-x^2) + O(x^20)) \\ _Colin Barker_, Jan 25 2016

%Y Cf. A142588 (Pell(3n)), A187361 (Pell(3n+1)).

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Mar 09 2011